Free Texas Instruments TI-83 Plus Calculator Guidebook PDF | Manualsnet (2024)

07/23/03 2001-2003 Texas Instruments

TI

TI-83 Plus /

TI-83 Plus Silver Edition

Graphing Calculator Guidebook

On/Off Graphing a function Menus Modes Using parentheses Lists

Tables Data and lists Matrices Split screen

Inferential statistics Archiving/Unarchiving Programming Menu maps

Sending and receiving Troubleshooting Formulas Support and service

More Information

First Steps

Creating

Beyond the Basics

TI-83 Plus

Important

Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an as-is basis.

In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

Windows is a registered trademark of Microsoft Corporation. Macintosh is a registered trademark of Apple Computer, Inc.

TI-83 Plus

US FCC Information Concerning Radio Frequency Interference

This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will not occur in a particular installation.

If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures: Reorient or relocate the receiving antenna. Increase the separation between the equipment and receiver. Connect the equipment into an outlet on a circuit different from that to

which the receiver is connected. Consult the dealer or an experienced radio/television technician for

help.

Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment.

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Chapter 1: Operating the TI-83 Plus Silver Edition

Documentation Conventions

In the body of this guidebook, TI-83 Plus (in silver) refers to the TI-83 Plus Silver Edition. Sometimes, as in Chapter 19, the full name TI-83 Plus Silver Edition is used to distinguish it from the TI-83 Plus.

All the instructions and examples in this guidebook also work for the TI-83 Plus. All the functions of the TI-83 Plus Silver Edition and the TI-83 Plus are the same. The two calculators differ only in available RAM memory and Flash application ROM memory.

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TI-83 Plus Keyboard

Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.

Keyboard Zones

Graphing Graphing keys access the interactive graphing features.

Editing Editing keys allow you to edit expressions and values.

Advanced Advanced function keys display menus that access the advanced functions.

Scientific Scientific calculator keys access the capabilities of a standard scientific calculator.

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TI-83 Plus

Editing Keys

Advanced Function Keys

Scientific Calculator Keys

Graphing Keys

Colors may vary in actual product.

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Using the Color.Coded Keyboard

The keys on the TI-83 Plus are color-coded to help you easily locate the key you need.

The light gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top set up and display graphs. The blue key provides access to applications such as the Finance application.

The primary function of each key is printed on the keys. For example, when you press , the MATH menu is displayed.

Using the y and Keys

The secondary function of each key is printed in yellow above the key. When you press the yellow y key, the character, abbreviation, or word printed in yellow above the other keys becomes active for the next keystroke. For example, when you press y and then , the TEST

menu is displayed. This guidebook describes this keystroke combination as y :.

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The alpha function of each key is printed in green above the key. When you press the green key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press and then , the letter A is entered. This guidebook describes this keystroke combination as [A].

The y key accesses the second function printed in yellow above each key.

The key accesses the alpha function printed in green above each key.

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Turning On and Turning Off the TI-83 Plus

Turning On the Calculator

To turn on the TI-83 Plus, press .

If you previously had turned off the calculator by pressing y M, the TI-83 Plus displays the home screen as it was when you last used it and clears any error.

If Automatic Power Down (APD) had previously turned off the calculator, the TI-83 Plus will return exactly as you left it, including the display, cursor, and any error.

If the TI-83 Plus is turned off and you connect it to another calculator or personal computer, the TI-83 Plus will wake up when you complete the connection.

If the TI-83 Plus is turned off and connected to another calculator or personal computer, any communication activity will wake up the TI-83 Plus.

To prolong the life of the batteries, APD turns off the TI-83 Plus automatically after about five minutes without any activity.

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Turning Off the Calculator

To turn off the TI-83 Plus manually, press y M.

All settings and memory contents are retained by Constant MemoryTM.

Any error condition is cleared.

Batteries

The TI-83 Plus uses four AAA alkaline batteries and has a user- replaceable backup lithium battery (CR1616 or CR1620). To replace batteries without losing any information stored in memory, follow the steps in Appendix B.

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Setting the Display Contrast

Adjusting the Display Contrast

You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark.

Note: The TI-83 Plus has 40 contrast settings, so each number 0 through 9 represents four settings.

The TI-83 Plus retains the contrast setting in memory when it is turned off.

To adjust the contrast, follow these steps.

1. Press and release the y key.

2. Press and hold or }, which are below and above the contrast symbol (yellow, half-shaded circle).

lightens the screen.

} darkens the screen.

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Note: If you adjust the contrast setting to 0, the display may become completely blank. To restore the screen, press and release y, and then press and hold } until the display reappears.

When to Replace Batteries

When the batteries are low, a low-battery message is displayed when you:

Turn on the calculator.

Download a new application.

Attempt to upgrade to new software.

To replace the batteries without losing any information in memory, follow the steps in Appendix B.

Generally, the calculator will continue to operate for one or two weeks after the low-battery message is first displayed. After this period, the TI-83 Plus will turn off automatically and the unit will not operate. Batteries must be replaced. All memory should be retained.

Note: The operating period following the first low-battery message could be longer than two weeks if you use the calculator infrequently.

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The Display

Types of Displays

The TI-83 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI-83 Plus can display a horizontally or vertically split screen to show graphs and text simultaneously.

Home Screen

The home screen is the primary screen of the TI-83 Plus. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen.

Displaying Entries and Answers

When text is displayed, the TI-83 Plus screen can display a maximum of 8 lines with a maximum of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display. If an expression on the home screen, the Y= editor (Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left.

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When an entry is executed on the home screen, the answer is displayed on the right side of the next line.

Entry Answer

The mode settings control the way the TI-83 Plus interprets expressions and displays answers.

If an answer, such as a list or matrix, is too long to display entirely on one line, an ellipsis (...) is displayed to the right or left. Press ~ and | to display the answer.

Entry Answer

Returning to the Home Screen

To return to the home screen from any other screen, press y 5.

Busy Indicator

When the TI-83 Plus is calculating or graphing, a vertical moving line is displayed as a busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line.

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Display Cursors

In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.

Cursor Appearance Effect of Next Keystroke

Entry Solid rectangle $

A character is entered at the cursor; any existing character is overwritten

Insert Underline __

A character is inserted in front of the cursor location

Second Reverse arrow

A 2nd character (yellow on the keyboard) is entered or a 2nd operation is executed

Alpha Reverse A

An alpha character (green on the keyboard) is entered or SOLVE is executed

Full Checkerboard rectangle #

No entry; the maximum characters are entered at a prompt or memory is full

If you press during an insertion, the cursor becomes an underlined A (A). If you press y during an insertion, the underlined cursor becomes an underlined # (#).

Graphs and editors sometimes display additional cursors, which are described in other chapters.

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Entering Expressions and Instructions

What Is an Expression?

An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI-83 Plus, you enter an expression in the same order as you would write it on paper. For example, pR2 is an expression.

You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.

Entering an Expression

To create an expression, you enter numbers, variables, and functions from the keyboard and menus. An expression is completed when you press , regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOS) rules, and the answer is displayed.

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Most TI-83 Plus functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press 45. Do not enter the letters L, O, and G. If you enter LOG, the TI-83 Plus interprets the entry as implied multiplication of the variables L, O, and G.

Calculate 3.76 (L7.9 + 5) + 2 log 45.

3 76 7 9 y C 5 2 45

Multiple Entries on a Line

To enter two or more expressions or instructions on a line, separate them with colons ( [:]). All instructions are stored together in last entry (ENTRY) .

Entering a Number in Scientific Notation

To enter a number in scientific notation, follow these steps.

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1. Enter the part of the number that precedes the exponent. This value can be an expression.

2. Press y D. is pasted to the cursor location.

3. If the exponent is negative, press , and then enter the exponent, which can be one or two digits.

When you enter a number in scientific notation, the TI-83 Plus does not automatically display answers in scientific or engineering notation. The mode settings and the size of the number determine the display format.

Functions

A function returns a value. For example, , L, +, (, and log( are the functions in the example on the previous page. In general, the first letter of each function is lowercase on the TI-83 Plus. Most functions take at least one argument, as indicated by an open parenthesis ( ( ) following the name. For example, sin( requires one argument, sin(value).

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Instructions

An instruction initiates an action. For example, ClrDraw is an instruction that clears any drawn elements from a graph. Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an open parenthesis ( ( ) at the end of the name. For example, Circle( requires three arguments, Circle(X,Y,radius).

Interrupting a Calculation

To interrupt a calculation or graph in progress, which is indicated by the busy indicator, press .

When you interrupt a calculation, a menu is displayed.

To return to the home screen, select 1:Quit.

To go to the location of the interruption, select 2:Goto.

When you interrupt a graph, a partial graph is displayed.

To return to the home screen, press or any nongraphing key.

To restart graphing, press a graphing key or select a graphing instruction.

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TI-83 Plus Edit Keys

Keystrokes Result

~ or | Moves the cursor within an expression; these keys repeat.

} or Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat.

On the top line of an expression on the home screen, } moves the cursor to the beginning of the expression.

On the bottom line of an expression on the home screen, moves the cursor to the end of the expression.

y | Moves the cursor to the beginning of an expression.

y ~ Moves the cursor to the end of an expression.

Evaluates an expression or executes an instruction.

On a line with text on the home screen, clears the current line.

On a blank line on the home screen, clears everything on the home screen.

In an editor, clears the expression or value where the cursor is located; it does not store a zero.

{ Deletes a character at the cursor; this key repeats.

y 6 Changes the cursor to an underline (__); inserts characters in front of the underline cursor; to end insertion, press y 6 or press |, }, ~, or .

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Keystrokes Result

y Changes the cursor to ; the next keystroke performs a 2nd operation (an operation in yellow above a key and to the left); to cancel 2nd, press y again.

Changes the cursor to ; the next keystroke pastes an alpha character (a character in green above a key and to the right) or executes SOLVE (Chapters 10 and 11); to cancel , press or press |, }, ~, or .

y 7 Changes the cursor to ; sets alpha-lock; subsequent keystrokes (on an alpha key) paste alpha characters; to cancel alpha-lock, press . If you are prompted to enter a name such as for a group or a program, alpha-lock is set automatically.

Pastes an X in Func mode, a T in Par mode, a q in Pol mode, or an n in Seq mode with one keystroke.

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Setting Modes

Checking Mode Settings

Mode settings control how the TI-83 Plus displays and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI-83 Plus is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings.

To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.

Normal Sci Eng Numeric notation Float 0123456789 Number of decimal places Radian Degree Unit of angle measure Func Par Pol Seq Type of graphing Connected Dot Whether to connect graph points Sequential Simul Whether to plot simultaneously Real a+bi re^qi Real, rectangular complex, or polar complex Full Horiz G-T Full screen, two split-screen modes

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Changing Mode Settings

To change mode settings, follow these steps.

1. Press or } to move the cursor to the line of the setting that you want to change.

2. Press ~ or | to move the cursor to the setting you want.

3. Press .

Setting a Mode from a Program

You can set a mode from a program by entering the name of the mode as an instruction; for example, Func or Float. From a blank program command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location.

Normal, Sci, Eng

Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any format.

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Normal notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in 12345.67.

Sci (scientific) notation mode expresses numbers in two parts. The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of E, as in 1.234567E4.

Eng (engineering) notation mode is similar to scientific notation. However, the number can have one, two, or three digits before the decimal; and the power-of-10 exponent is a multiple of three, as in 12.34567E3.

Note: If you select Normal notation, but the answer cannot display in 10 digits (or the absolute value is less than .001), the TI-83 Plus expresses the answer in scientific notation.

Float, 0123456789

Float (floating) decimal mode displays up to 10 digits, plus the sign and decimal.

0123456789 (fixed) decimal mode specifies the number of digits (0 through 9) to display to the right of the decimal. Place the cursor on the desired number of decimal digits, and then press .

The decimal setting applies to Normal, Sci, and Eng notation modes.

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The decimal setting applies to these numbers:

An answer displayed on the home screen

Coordinates on a graph (Chapters 3, 4, 5, and 6)

The Tangent( DRAW instruction equation of the line, x, and dy/dx values (Chapter 8)

Results of CALCULATE operations (Chapters 3, 4, 5, and 6)

The regression equation stored after the execution of a regression model (Chapter 12)

Radian, Degree

Angle modes control how the TI-83 Plus interprets angle values in trigonometric functions and polar/rectangular conversions.

Radian mode interprets angle values as radians. Answers display in radians.

Degree mode interprets angle values as degrees. Answers display in degrees.

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Func, Par, Pol, Seq

Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes in detail.

Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3).

Par (parametric) graphing mode plots relations, where X and Y are functions of T (Chapter 4).

Pol (polar) graphing mode plots functions, where r is a function of q (Chapter 5).

Seq (sequence) graphing mode plots sequences (Chapter 6).

Connected, Dot

Connected plotting mode draws a line connecting each point calculated for the selected functions.

Dot plotting mode plots only the calculated points of the selected functions.

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Sequential, Simul

Sequential graphing-order mode evaluates and plots one function completely before the next function is evaluated and plotted.

Simul (simultaneous) graphing-order mode evaluates and plots all selected functions for a single value of X and then evaluates and plots them for the next value of X.

Note: Regardless of which graphing mode is selected, the TI-83 Plus will sequentially graph all stat plots before it graphs any functions.

Real, a+bi, re^qi

Real mode does not display complex results unless complex numbers are entered as input.

Two complex modes display complex results.

a+bi (rectangular complex mode) displays complex numbers in the form a+bi.

re^qi (polar complex mode) displays complex numbers in the form re^qi.

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Full, Horiz, G.T

Full screen mode uses the entire screen to display a graph or edit screen.

Each split-screen mode displays two screens simultaneously.

Horiz (horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9).

G.T (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).

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Using TI-83 Plus Variable Names

Variables and Defined Items

On the TI-83 Plus you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings.

The TI-83 Plus uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names.

Variable Type Names

Real numbers A, B, ... , Z

Complex numbers A, B, ... , Z

Matrices A, B, C, ... , J

Lists L1, L2, L3, L4, L5, L6, and user-defined names

Functions Y1, Y2, . . . , Y9, Y0

Parametric equations X1T and Y1T, . . . , X6T and Y6T

Polar functions r1, r2, r3, r4, r5, r6

Sequence functions u, v, w

Stat plots Plot1, Plot2, Plot3

Graph databases GDB1, GDB2, . . . , GDB9, GDB0

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Variable Type Names

Graph pictures Pic1, Pic2, ... , Pic9, Pic0

Strings Str1, Str2, ... , Str9, Str0

Apps Applications

AppVars Application variables

Groups Grouped variables

System variables Xmin, Xmax, and others

Notes about Variables

You can create as many list names as memory will allow (Chapter 11).

Programs have user-defined names and share memory with variables (Chapter 16).

From the home screen or from a program, you can store to matrices (Chapter 10), lists (Chapter 11), strings (Chapter 15), system variables such as Xmax (Chapter 1), TblStart (Chapter 7), and all Y= functions (Chapters 3, 4, 5, and 6).

From an editor, you can store to matrices, lists, and Y= functions (Chapter 3).

From the home screen, a program, or an editor, you can store a value to a matrix element or a list element.

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You can use DRAW STO menu items to store and recall graph databases and pictures (Chapter 8).

Although most variables can be archived, system variables including r, t, x, y, and q cannot be archived (Chapter 18)

Apps are independent applications.which are stored in Flash ROM. AppVars is a variable holder used to store variables created by independent applications. You cannot edit or change variables in AppVars unless you do so through the application which created them.

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Storing Variable Values

Storing Values in a Variable

Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used.

To store a value to a variable from the home screen or a program using the key, begin on a blank line and follow these steps.

1. Enter the value you want to store. The value can be an expression.

2. Press . ! is copied to the cursor location.

3. Press and then the letter of the variable to which you want to store the value.

4. Press . If you entered an expression, it is evaluated. The value is stored to the variable.

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Displaying a Variable Value

To display the value of a variable, enter the name on a blank line on the home screen, and then press .

Archiving Variables (Archive, Unarchive)

You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently. Archived variables are indicated by asterisks (*) to the left of the variable names. Archived variables cannot be edited or executed. They can only be seen and unarchived. For example, if you archive list L1, you will see that L1 exists in memory but if you select it and paste the name L1 to the home screen, you wont be able to see its contents or edit it until they are unarchived.

.

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Recalling Variable Values

Using Recall (RCL)

To recall and copy variable contents to the current cursor location, follow these steps. To leave RCL, press .

1. Press y RCL. RCL and the edit cursor are displayed on the bottom line of the screen.

2. Enter the name of the variable in any of five ways.

Press and then the letter of the variable.

Press y LIST, and then select the name of the list, or press y [Ln].

Press y >, and then select the name of the matrix.

Press to display the VARS menu or ~ to display the VARS Y.VARS menu; then select the type and then the name of the variable or function.

Press |, and then select the name of the program (in the program editor only).

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The variable name you selected is displayed on the bottom line and the cursor disappears.

3. Press . The variable contents are inserted where the cursor was located before you began these steps.

Note: You can edit the characters pasted to the expression without affecting the value in memory.

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ENTRY (Last Entry) Storage Area

Using ENTRY (Last Entry)

When you press on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI-83 Plus, ENTRY is retained in memory.

To recall ENTRY, press y [. The last entry is pasted to the current cursor location, where you can edit and execute it. On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line.

Because the TI-83 Plus updates ENTRY only when you press , you can recall the previous entry even if you have begun to enter the next expression.

5 7 y [

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Accessing a Previous Entry

The TI-83 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll those entries, press y [ repeatedly. If a single entry is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area.

1 A 2 B y [

If you press y [ after displaying the oldest stored entry, the newest stored entry is displayed again, then the next-newest entry, and so on.

y [

Reexecuting the Previous Entry

After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press .

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To reexecute the displayed entry, press again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed.

0 N N 1 N : N

Multiple Entry Values on a Line

To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press . All expressions and instructions separated by colons are stored in ENTRY.

When you press y [, all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press .

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For the equation A=pr2, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess.

8 R [:] y B R y [

y | 7 y 6 95

Continue until the answer is as accurate as you want.

Clearing ENTRY

Clear Entries (Chapter 18) clears all data that the TI-83 Plus is holding in the ENTRY storage area.

Using Ans in an Expression

When an expression is evaluated successfully from the home screen or from a program, the TI-83 Plus stores the answer to a storage area called Ans (last answer). Ans may be a real or complex number, a list, a matrix, or a string. When you turn off the TI-83 Plus, the value in Ans is retained in memory.

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You can use the variable Ans to represent the last answer in most places. Press y Z to copy the variable name Ans to the cursor location. When the expression is evaluated, the TI-83 Plus uses the value of Ans in the calculation.

Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.

1 7 4 2 147 y Z

Continuing an Expression

You can use Ans as the first entry in the next expression without entering the value again or pressing y Z. On a blank line on the home screen, enter the function. The TI-83 Plus pastes the variable name Ans to the screen, then the function.

5 2 9 9

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Storing Answers

To store an answer, store Ans to a variable before you evaluate another expression.

Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V.

y B 5 3 3 V

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TI-83 Plus Menus

Using a TI-83 Plus Menu

You can access most TI-83 Plus operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen.

The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item 1, which also is highlighted.

A number or letter identifies each menu items place in the menu. The order is 1 through 9, then 0, then A, B, C, and so on. The LIST NAMES, PRGM EXEC, and PRGM EDIT menus only label items 1 through 9 and 0.

When the menu continues beyond the displayed items, a down arrow ($) replaces the colon next to the last displayed item.

When a menu item ends in an ellipsis (...), the item displays a secondary menu or editor when you select it.

When an asterisk (*) appears to the left of a menu item, that item is stored in user data archive (Chapter 18).

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To display any other menu listed on the top line, press ~ or | until that menu name is highlighted. The cursor location within the initial menu is irrelevant. The menu is displayed with the cursor on the first item.

Note: The Menu Map in Appendix A shows each menu, each operation under each menu, and the key or key combination you press to display each menu.

Displaying a Menu

While using your TI-83 Plus, you often will need to access items from its menus.

When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press , the MATH menu is displayed as a full screen.

After you select an item from a menu, the screen where you are working usually is displayed again.

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Moving from One Menu to Another

Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press ~ and | to highlight each menu name.

Scrolling a Menu

To scroll down the menu items, press . To scroll up the menu items, press }.

To page down six menu items at a time, press . To page up six menu items at a time, press }. The green arrows on the calculator, between and }, are the page-down and page-up symbols.

To wrap to the last menu item directly from the first menu item, press }. To wrap to the first menu item directly from the last menu item, press .

Selecting an Item from a Menu

You can select an item from a menu in either of two ways.

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Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen.

Press or } to move the cursor to the item you want, and then press .

After you select an item from a menu, the TI-83 Plus typically displays the previous screen.

Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9 and 0 are labeled in such a way that you can select them by pressing the appropriate number key. To move the cursor to the first item beginning with any alpha character or q, press the key combination for that alpha character or q. If no items begin with that character, the cursor moves beyond it to the next item.

Calculate 327.

27

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Leaving a Menu without Making a Selection

You can leave a menu without making a selection in any of four ways.

Press y 5 to return to the home screen.

Press to return to the previous screen.

Press a key or key combination for a different menu, such as or y 9.

Press a key or key combination for a different screen, such as o or y 0.

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VARS and VARS Y.VARS Menus

VARS Menu

You can enter the names of functions and system variables in an expression or store to them directly.

To display the VARS menu, press . All VARS menu items display secondary menus, which show the names of the system variables. 1:Window, 2:Zoom, and 5:Statistics each access more than one secondary menu.

VARS Y-VARS 1: Window... X/Y, T/q, and U/V/W variables 2: Zoom... ZX/ZY, ZT/Zq, and ZU variables 3: GDB... Graph database variables 4: Picture... Picture variables 5: Statistics... XY, G, EQ, TEST, and PTS variables 6: Table... TABLE variables 7: String... String variables

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Selecting a Variable from the VARS Menu or VARS Y.VARS Menu

To display the VARS Y.VARS menu, press ~. 1:Function, 2:Parametric, and 3:Polar display secondary menus of the Y= function variables.

VARS Y-VARS

1: Function... Yn functions 2: Parametric... XnT, YnT functions 3: Polar... rn functions 4: On/Off... Lets you select/deselect functions

Note: The sequence variables (u, v, w) are located on the keyboard as the second functions of , , and .

To select a variable from the VARS or VARS Y.VARS menu, follow these steps.

1. Display the VARS or VARS Y.VARS menu.

Press to display the VARS menu.

Press ~ to display the VARS Y.VARS menu.

2. Select the type of variable, such as 2:Zoom from the VARS menu or 3:Polar from the VARS Y.VARS menu. A secondary menu is displayed.

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3. If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can press ~ or | to display other secondary menus.

4. Select a variable name from the menu. It is pasted to the cursor location.

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Equation Operating System (EOS)

Order of Evaluation

The Equation Operating System (EOS) defines the order in which functions in expressions are entered and evaluated on the TI-83 Plus. EOS lets you enter numbers and functions in a simple, straightforward sequence.

EOS evaluates the functions in an expression in this order.

Order Number Function

1 Functions that precede the argument, such as (, sin(, or log(

2 Functions that are entered after the argument, such as 2, M1, !, , r, and conversions

3 Powers and roots, such as 2^5 or 5x32

4 Permutations (nPr) and combinations (nCr)

5 Multiplication, implied multiplication, and division

6 Addition and subtraction

7 Relational functions, such as > or

8 Logic operator and

9 Logic operators or and xor

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Note: Within a priority level, EOS evaluates functions from left to right. Calculations within parentheses are evaluated first.

Implied Multiplication

The TI-83 Plus recognizes implied multiplication, so you need not press to express multiplication in all cases. For example, the TI-83 Plus interprets 2p, 4sin(46), 5(1+2), and (25)7 as implied multiplication.

Note: TI-83 Plus implied multiplication rules, although like theTI.83, differ from those of the TI.82. For example, the TI-83 Plus evaluates 12X as (12)X, while the TI.82 evaluates 12X as 1/(2X) (Chapter 2).

Parentheses

All calculations inside a pair of parentheses are completed first. For example, in the expression 4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then multiplies the answer, 3, by 4.

You can omit the close parenthesis ( ) ) at the end of an expression. All open parenthetical elements are closed automatically at the end of an expression. This is also true for open parenthetical elements that precede the store or display-conversion instructions.

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Note: An open parenthesis following a list name, matrix name, or Y= function name does not indicate implied multiplication. It specifies elements in the list (Chapter 11) or matrix (Chapter 10) and specifies a value for which to solve the Y= function.

Negation

To enter a negative number, use the negation key. Press and then enter the number. On the TI-83 Plus, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation.

For example, MX2, evaluates to a negative number (or 0). Use parentheses to square a negative number.

Note: Use the key for subtraction and the key for negation. If you press to enter a negative number, as in 9 7, or if you press to indicate subtraction, as in 9 7, an error occurs. If you press A B, it is interpreted as implied multiplication (AMB).

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Special Features of the TI-83 Plus

Flash Electronic Upgradability

The TI-83 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new calculator.

For details, refer to: Chapter 19

As new functionality becomes available, you can electronically upgrade your TI-83 Plus from the Internet. Future software versions include maintenance upgrades that will be released free of charge, as well as new applications and major software upgrades that will be available for purchase from the TI web site: education.ti.com

1.56 Megabytes (M) of Available Memory

1.56 M of available memory are built into the TI-83 Plus. About 24 kilobytes (K) of RAM (random access memory) are available for you to compute and store functions, programs, and data.

For details, refer to: Chapter 18

About 1.54 M of user data archive allow you to store data, programs, applications, or any other variables to a safe location where they cannot

TI-83 Plus Operating the TI-83 Plus Silver Edition 51

be edited or deleted inadvertently. You can also free up RAM by archiving variables to user data

Applications

Applications can be installed to customize the TI-83 Plus to your classroom needs. The big 1.54 M archive space lets you store up to 94 applications at one time. Applications can also be stored on a computer for later use or linked unit-to-unit.

For details, refer to: Chapter 18

Archiving

You can store variables in the TI-83 Plus user data archive, a protected area of memory separate from RAM. The user data archive lets you:

For details, refer to: Chapter 18

Store data, programs, applications or any other variables to a safe location where they cannot be edited or deleted inadvertently.

Create additional free RAM by archiving variables.

By archiving variables that do not need to be edited frequently, you can free up RAM for applications that may require additional memory.

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Calculator-Based Laboratory (CBL 2, CBL) and Calculator-Based Ranger (CBR)

The TI-83 Plus comes with the CBL/CBR application already installed. When coupled with the (optional) CBL 2/CBL or CBR accessories, you can use the TI-83 Plus to analyze real world data.

For details, refer to: Chapter 14

CBL 2/CBL and CBR let you explore mathematical and scientific relationships among distance, velocity, acceleration, and time using data collected from activities you perform.

CBL 2/CBL and CBR differ in that CBL 2/CBL allows you to collect data using several different probes analyzing temperature, light, voltage, or sonic (motion) data. CBR collects data using a built-in Sonic probe. CBL 2/CBL and CBR accessories can be linked together to collect more than one type of data at the same time. You can find more information on CBL 2/CBL and CBR in their user manuals.

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Other TI-83 Plus Features

Getting Started has introduced you to basic TI-83 Plus operations. This guidebook covers the other features and capabilities of the TI-83 Plus in greater detail.

Graphing

You can store, graph, and analyze up to 10 functions, up to six parametric functions, up to six polar functions, and up to three sequences. You can use DRAW instructions to annotate graphs.

For graphing details, refer to: Chapters 3, 4, 5, 6, 8

The graphing chapters appear in this order: Function, Parametric, Polar, Sequence, and DRAW.

Sequences

You can generate sequences and graph them over time. Or, you can graph them as web plots or as phase plots.

For details, refer to: Chapter 6

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Tables

You can create function evaluation tables to analyze many functions simultaneously.

For details, refer to: Chapter 7

Split Screen

You can split the screen horizontally to display both a graph and a related editor (such as the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously.

For details, refer to: Chapter 9

Matrices

You can enter and save up to 10 matrices and perform standard matrix operations on them.

For details, refer to: Chapter 10

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Lists

You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves.

For details, refer to: Chapter 11

Statistics

You can perform one- and two-variable, list- based statistical analyses, including logistic and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regular box-and-whisker plot, or normal probability plot. You can define and store up to three stat plot definitions.

For details, refer to: Chapter 12

Inferential Statistics

You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically.

For details, refer to: Chapter 13

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Applications

You can use such applications as Finance or the CBL/CBR. With the Finance application you can use time-value-of-money (TVM) functions to analyze financial instruments such as annuities,

For details, refer to: Chapter 14

loans, mortgages, leases, and savings. You can analyze the value of money over equal time periods using cash flow functions. You can amortize loans with the amortization functions. With the CBL/CBR applications and CBL 2/CBL or CBR (optional) accessories, you can use a variety of probes to collect real world data.

Your TI-83 Plus includes Flash applications in addition to the ones mentioned above. Press to see the complete list of applications that came with your calculator.

Documentation for TI Flash applications is on the TI Resource CD. Visit education.ti.com/calc/guides for additional Flash application guidebooks.

CATALOG

The CATALOG is a convenient, alphabetical list of all functions and instructions on the TI-83 Plus. You can paste any function or instruction from the CATALOG to the current cursor location.

For details, refer to: Chapter 15

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Programming

You can enter and store programs that include extensive control and input/output instructions.

For details, refer to: Chapter 16

Archiving

Archiving allows you to store data, programs, or other variables to user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory.

For details, refer to: Chapter 16

Archived variables are indicated by asterisks (*) to the left of the variable names.

Communication Link

The TI-83 Plus has a port to connect and communicate with another TI-83 Plus, a TI-83 Plus, a TI.83, a TI-82, a TI-73, CBL 2/CBL, or a CBR System.

For details, refer to: Chapter 19

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With the TI Connect or TI-GRAPH LINK software and a TI-GRAPH LINK cable, you can also link the TI-83 Plus to a personal computer.

As future software upgrades become available on the TI web site, you can download the software to your PC and then use the TI Connect or TI-GRAPH LINK software and a TI-GRAPH LINK cable to upgrade your TI-83 Plus.

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Error Conditions

Diagnosing an Error

The TI-83 Plus detects errors while performing these tasks.

Evaluating an expression

Executing an instruction

Plotting a graph

Storing a value

When the TI-83 Plus detects an error, it returns an error message as a menu title, such as ERR:SYNTAX or ERR:DOMAIN. Appendix B describes each error type and possible reasons for the error.

If you select 1:Quit (or press y 5 or ), then the home screen is displayed.

If you select 2:Goto, then the previous screen is displayed with the cursor at or near the error location.

Note: If a syntax error occurs in the contents of a Y= function during program execution, then the Goto option returns to the Y= editor, not to the program.

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Correcting an Error

To correct an error, follow these steps.

1. Note the error type (ERR:error type).

2. Select 2:Goto, if it is available. The previous screen is displayed with the cursor at or near the error location.

3. Determine the error. If you cannot recognize the error, refer to Appendix B.

4. Correct the expression.

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Chapter 2: Math, Angle, and Test Operations

Getting Started: Coin Flip

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5.

1. Begin on the home screen. Press | to display the MATH PRB menu. Press 7 to select 7:randBin( (random Binomial). randBin( is pasted to the home screen. Press 10 to enter the number of coin flips. Press . Press 5 to enter the probability of heads. Press . Press 40 to enter the number of simulations. Press .

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2. Press to evaluate the expression. A list of 40 elements is generated with the first 7 displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on.

3. Press ~ or | to view the additional counts in the list. Ellipses (...) indicate that the list continues beyond the screen.

4. Press y L1 to store the data to the list name L1. You then can use the data for another activity, such as plotting a histogram (Chapter 12).

Note: Since randBin( generates random numbers, your list elements may differ from those in the example.

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Keyboard Math Operations

Using Lists with Math Operations

Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length.

+ (Addition), N (Subtraction), (Multiplication), (Division)

You can use + (addition, ), N (subtraction, ), (multiplication, ), and (division, ) with real and complex numbers, expressions, lists, and matrices. You cannot use with matrices.

valueA+valueB valueA N valueB valueAvalueB valueA valueB

Trigonometric Functions

You can use the trigonometric (trig) functions (sine, ; cosine, ; and tangent, ) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. For example, sin(30) in Radian mode returns L.9880316241; in Degree mode it returns .5.

TI-83 Plus Math, Angle, and Test Operations 64

sin(value) cos(value) tan(value)

You can use the inverse trig functions (arcsine, y ?; arccosine, y @; and arctangent, y A) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.

sinL1(value) cosL1(value) tanL1(value)

Note: The trig functions do not operate on complex numbers.

^ (Power), 2 (Square), ( (Square Root)

You can use ^ (power, ), 2 (square, ), and ( (square root, y C) with real and complex numbers, expressions, lists, and matrices. You cannot use ( with matrices.

value^power value2 (value)

L1 (Inverse)

You can use L1 (inverse, ) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1x.

valueL1

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log(, 10^(, ln(

You can use log( (logarithm, ), 10^( (power of 10, y G), and ln( (natural log, ) with real or complex numbers, expressions, and lists.

log(value) 10^(power) ln(value)

e^( (Exponential)

e^( (exponential, y J) returns the constant e raised to a power. You can use e^( with real or complex numbers, expressions, and lists.

e^(power)

e (Constant)

e (constant, y [e]) is stored as a constant on the TI-83 Plus. Press y [e] to copy e to the cursor location. In calculations, the TI-83 Plus uses 2.718281828459 for e.

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L (Negation)

M (negation, ) returns the negative of value. You can use M with real or complex numbers, expressions, lists, and matrices.

Mvalue

EOS rules (Chapter 1) determine when negation is evaluated. For example, LA2 returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in (LA)2.

Note: On the TI-83 Plus, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press .

p (Pi)

p (Pi, y B) is stored as a constant in the TI-83 Plus. In calculations, the TI-83 Plus uses 3.1415926535898 for p.

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MATH Operations

MATH Menu

To display the MATH menu, press .

MATH NUM CPX PRB

1: 4Frac Displays the answer as a fraction. 2: 4Dec Displays the answer as a decimal. 3: 3 Calculates the cube. 4: 3( Calculates the cube root. 5: x Calculates the xth root. 6: fMin( Finds the minimum of a function. 7: fMax( Finds the maximum of a function. 8: nDeriv( Computes the numerical derivative. 9: fnInt( Computes the function integral. 0: Solver... Displays the equation solver.

4Frac, 4Dec

4Frac (display as a fraction) displays an answer as its rational equivalent. You can use 4Frac with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use 4Frac following value.

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value 4Frac

4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with real or complex numbers, expressions, lists, and matrices. You can only use 4Dec following value.

value 4Dec

3(Cube), 3( (Cube Root)

3 (cube) returns the cube of value. You can use 3 with real or complex numbers, expressions, lists, and square matrices.

value3

3( (cube root) returns the cube root of value. You can use 3( with real or complex numbers, expressions, and lists.

3(value)

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x (Root)

x (xth root) returns the xth root of value. You can use x with real or complex numbers, expressions, and lists.

xthrootxvalue

fMin(, fMax(

fMin( (function minimum) and fMax( (function maximum) return the value at which the local minimum or local maximum value of expression with respect to variable occurs, between lower and upper values for variable. fMin( and fMax( are not valid in expression. The accuracy is controlled by tolerance (if not specified, the default is 1L5).

fMin(expression,variable,lower,upper[,tolerance]) fMax(expression,variable,lower,upper[,tolerance])

Note: In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]).

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nDeriv(

nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1L3). nDeriv( is valid only for real numbers.

nDeriv(expression,variable,value[,H])

nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.

2

)(()( )('

+= xfxf xf

As H becomes smaller, the approximation usually becomes more accurate.

You can use nDeriv( once in expression. Because of the method used to calculate nDeriv(, the TI-83 Plus can return a false derivative value at a nondifferentiable point.

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fnInt(

fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of expression with respect to variable, given lower limit, upper limit, and a tolerance (if not specified, the default is 1L5). fnInt( is valid only for real numbers.

fnInt(expression,variable,lower,upper[,tolerance])

Tip: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s.

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Using the Equation Solver

Solver

Solver displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero. Solver is valid only for real numbers.

When you select Solver, one of two screens is displayed.

The equation editor (see step 1 picture below) is displayed when the equation variable eqn is empty.

The interactive solver editor is displayed when an equation is stored in eqn.

Entering an Expression in the Equation Solver

To enter an expression in the equation solver, assuming that the variable eqn is empty, follow these steps.

1. Select 0:Solver from the MATH menu to display the equation editor.

2. Enter the expression in any of three ways.

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Enter the expression directly into the equation solver.

Paste a Y= variable name from the VARS Y.VARS menu to the equation solver.

Press y K, paste a Y= variable name from the VARS Y.VARS

menu, and press . The expression is pasted to the equation solver.

The expression is stored to the variable eqn as you enter it.

3. Press or . The interactive solver editor is displayed.

The equation stored in eqn is set equal to zero and displayed on the top line.

Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed.

The default lower and upper bounds appear in the last line of the editor (bound={L199,199}).

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A $ is displayed in the first column of the bottom line if the editor continues beyond the screen.

Tip: To use the solver to solve an equation such as K=.5MV2, enter eqn:0=KN.5MV2 in the equation editor.

Entering and Editing Variable Values

When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable.

You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration.

You can store equations to any VARS Y.VARS variables, such as Y1 or r6, and then reference the variables in the equation. The interactive solver editor displays all variables of all Y= functions referenced in the equation.

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Solving for a Variable in the Equation Solver

To solve for a variable using the equation solver after an equation has been stored to eqn, follow these steps.

1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not already displayed.

2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press or .

3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-83 Plus will attempt to display the solution that is closest to your guess.

TI-83 Plus Math, Angle, and Test Operations 76

The default guess is calculated as (upper+lower)

2 .

4. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-83 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={L199,199}.

5. Move the cursor to the variable for which you want to solve and press \ (above the key).

The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen. Note: When a number continues beyond the screen, be sure to press ~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent.

The values of the variables are updated in memory.

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leftNrt=diff is displayed in the last line of the editor. diff is the difference between the left and right sides of the equation. A solid square in the first column next to leftNrt= indicates that the equation has been evaluated at the new value of the variable for which you solved.

Editing an Equation Stored to eqn

To edit or replace an equation stored to eqn when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation.

Equations with Multiple Roots

Some equations have more than one solution. You can enter a new initial guess or new bounds to look for additional solutions.

Further Solutions

After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid squares next to the previous solution and leftNrt=diff disappear. Move the cursor to the variable for which you now want to solve and press \.

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Controlling the Solution for Solver or solve(

The TI-83 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions.

Using solve( on the Home Screen or from a Program

The function solve( is available only from CATALOG or from within a program. It returns a solution (root) of expression for variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default for lower is L199. The default for upper is 199. solve( is valid only for real numbers.

solve(expression,variable,guess[,{lower,upper}])

expression is assumed equal to zero. The value of variable will not be updated in memory. guess may be a value or a list of two values. Values must be stored for every variable in expression, except variable, before expression is evaluated. lower and upper must be entered in list format.

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MATH NUM (Number) Operations

MATH NUM Menu

To display the MATH NUM menu, press ~.

MATH NUM CPX PRB 1: abs( Absolute value 2: round( Round 3: iPart( Integer part 4: fPart( Fractional part 5: int( Greatest integer 6: min( Minimum value 7: max( Maximum value 8: lcm( Least common multiple 9: gcd( Greatest common divisor

abs(

abs( (absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices.

abs(value)

Note: abs( is also available on the MATH CPX menu.

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round(

round( returns a number, expression, list, or matrix rounded to #decimals (9). If #decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits.

round(value[,#decimals])

iPart(, fPart(

iPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices.

iPart(value)

fPart( (fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices.

fPart(value)

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int(

int( (greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices.

int(value)

Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbers and negative integers, but one integer less than the result of iPart( for negative noninteger numbers.

min(, max(

min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list. If listA and listB are compared, min( returns a list of the smaller of each pair of elements. If list and value are compared, min( compares each element in list with value.

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max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared, max( returns a list of the larger of each pair of elements. If list and value are compared, max( compares each element in list with value.

min(valueA,valueB) max(valueA,valueB) min(list) max(list) min(listA,listB) max(listA,listB) min(list,value) max(list,value)

Note: min( and max( also are available on the LIST MATH menu.

lcm(, gcd(

lcm( returns the least common multiple of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, lcm( returns a list of the lcm of each pair of elements. If list and value are specified, lcm( finds the lcm of each element in list and value.

gcd( returns the greatest common divisor of valueA and valueB, both of which must be nonnegative integers. When listA and listB are specified, gcd( returns a list of the gcd of each pair of elements. If list and value are specified, gcd( finds the gcd of each element in list and value.

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lcm(valueA,valueB) gcd(valueA,valueB) lcm(listA,listB) gcd(listA,listB) lcm(list,value) gcd(list,value)

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Entering and Using Complex Numbers

Complex-Number Modes

The TI-83 Plus displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes.

a+bi (rectangular-complex mode) re^qi (polar-complex mode)

On the TI-83 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements.

In Real mode, complex-number results return an error, unless you entered a complex number as input. For example, in Real mode ln(L1) returns an error; in a+bi mode ln(L1) returns an answer.

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Real mode a+bi mode

$ $

Entering Complex Numbers

Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed.

Note about Radian Versus Degree Mode

Radian mode is recommended for complex number calculations. Internally, the TI-83 Plus converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions.

In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^() are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode.

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Interpreting Complex Results

Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction. In the example below, polar-complex (re^qi) and Radian modes are set.

Rectangular-Complex Mode

Rectangular-complex mode recognizes and displays a complex number in the form a+bi, where a is the real component, b is the imaginary component, and i is a constant equal to -1.

To enter a complex number in rectangular form, enter the value of a (real component), press or , enter the value of b (imaginary component), and press y V (constant).

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real component(+ or N)imaginary component i

Polar-Complex Mode

Polar-complex mode recognizes and displays a complex number in the form re^qi, where r is the magnitude, e is the base of the natural log, q is the angle, and i is a constant equal to -1.

To enter a complex number in polar form, enter the value of r (magnitude), press y J (exponential function), enter the value of q (angle), press y V (constant), and then press .

magnitudee^(anglei)

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MATH CPX (Complex) Operations

MATH CPX Menu

To display the MATH CPX menu, press ~ ~.

MATH NUM CPX PRB 1: conj( Returns the complex conjugate. 2: real( Returns the real part. 3: imag( Returns the imaginary part. 4: angle( Returns the polar angle. 5: abs( Returns the magnitude (modulus). 6: 4Rect Displays the result in rectangular form. 7: 4Polar Displays the result in polar form.

conj(

conj( (conjugate) returns the complex conjugate of a complex number or list of complex numbers.

conj(a+bi) returns aNbi in a+bi mode. conj(re^(qi)) returns re^(Lqi) in re^qi mode.

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real(

real( (real part) returns the real part of a complex number or list of complex numbers.

real(a+bi) returns a. real(re^(qi)) returns rcos(q).

imag(

imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers.

imag(a+bi) returns b. imag(re^(qi)) returns rsin(q).

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angle(

angle( returns the polar angle of a complex number or list of complex numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant.

angle(a+bi) returns tanL1(b/a). angle(re^(qi)) returns q, where Lp

abs(

abs( (absolute value) returns the magnitude (modulus), (real2+imag2) , of a complex number or list of complex numbers.

abs(a+bi) returns (a2+b2) . abs(re^(qi)) returns r (magnitude).

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4Rect

4Rect (display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real.

complex result8Rect returns a+bi.

4Polar

4Polar (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real.

complex result8Polar returns re^(qi).

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MATH PRB (Probability) Operations

MATH PRB Menu

To display the MATH PRB menu, press |.

MATH NUM CPX PRB

1: rand Random-number generator 2: nPr Number of permutations 3: nCr Number of combinations 4: ! Factorial 5: randInt( Random-integer generator 6: randNorm( Random # from Normal distribution 7: randBin( Random # from Binomial distribution

rand

rand (random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of random-numbers, specify an integer > 1 for numtrials (number of trials). The default for numtrials is 1.

rand[(numtrials)]

Tip: To generate random numbers beyond the range of 0 to 1, you can include rand in an expression. For example, rand5 generates a random number > 0 and < 5.

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With each rand execution, the TI-83 Plus generates the same random- number sequence for a given seed value. The TI-83 Plus factory-set seed value for rand is 0. To generate a different random-number sequence, store any nonzero seed value to rand. To restore the factory- set seed value, store 0 to rand or reset the defaults (Chapter 18).

Note: The seed value also affects randInt(, randNorm(, and randBin( instructions.

nPr, nCr

nPr (number of permutations) returns the number of permutations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists.

items nPr number

nCr (number of combinations) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists.

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items nCr number

! (Factorial)

! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be L.5 and 69.

value!

Note: The factorial is computed recursively using the relationship (n+1)! = nn!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L12)!=p is used to complete the calculation. Hence:

n!=n(nN1)(nN2) ... 21, if n is an integer 0 n!= n(nN1)(nN2) ... 12p, if n+12 is an integer 0 n! is an error, if neither n nor n+12 is an integer 0.

(The variable n equals value in the syntax description above.)

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randInt(

randInt( (random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer >1 for numtrials (number of trials); if not specified, the default is 1.

randInt(lower,upper[,numtrials])

randNorm(

randNorm( (random Normal) generates and displays a random real number from a specified Normal distribution. Each generated value could be any real number, but most will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1.

randNorm(m,s[,numtrials])

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randBin(

randBin( (random Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials (number of trials) must be 1. prob (probability of success) must be 0 and 1. To generate a list of random numbers, specify an integer > 1 for numsimulations (number of simulations); if not specified, the default is 1.

randBin(numtrials,prob[,numsimulations])

Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin( instructions.

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ANGLE Operations

ANGLE Menu

To display the ANGLE menu, press y [ANGLE]. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI-83 Pluss interpretation of ANGLE menu entries.

ANGLE

1: Degree notation 2: ' DMS minute notation 3: r Radian notation 4: 8DMS Displays as degree/minute/second 5: R8Pr( Returns r, given X and Y 6: R8Pq( Returns q, given X and Y 7: P8Rx( Returns x, given R and q

8: P8Ry( Returns y, given R and q

Entry Notation

DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (), the minute symbol ('), and the second symbol ("). degrees must be a real number; minutes and seconds must be real numbers 0.

degreesminutes'seconds"

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For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to Degree, you must use so that the TI-83 Plus can interpret the argument as degrees, minutes, and seconds.

Degree mode Radian mode

(Degree)

(degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use to convert degrees to radians.

value

{value1,value2,value3,value4,...,value n}

also designates degrees (D) in DMS format. ' (minutes) designates minutes (M) in DMS format. " (seconds) designates seconds (S) in DMS format.

Note: " is not on the ANGLE menu. To enter ", press [].

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r (Radians)

r (radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use r to convert radians to degrees.

valuer

Degree mode

8DMS

8DMS (degree/minute/second) displays answer in DMS format. The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of a line.

answer8DMS

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R8Pr(, R8Pq(, P8Rx(, P8Ry(

R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq( converts rectangular coordinates to polar coordinates and returns q. x and y can be lists.

R8Pr(x,y), R8Pq(x,y)

Note: Radian mode is set.

P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polar coordinates to rectangular coordinates and returns y. r and q can be lists.

P8Rx(r,q), P8Ry(r,q)

Note: Radian mode is set.

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TEST (Relational) Operations

TEST Menu

To display the TEST menu, press y :.

This operator... Returns 1 (true) if... TEST LOGIC

1: = Equal 2: Not equal to 3: > Greater than 4: Greater than or equal to 5: < Less than 6: Less than or equal to

=, , >, , <,

Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be real numbers, expressions, or lists. For = and only, valueA and valueB also can be matrices or complex numbers. If valueA and valueB are matrices, both must have the same dimensions.

Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.

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valueA=valueB valueAvalueB valueA>valueB valueAvalueB valueA<valueB valueAvalueB

Using Tests

Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1).

The expression 2+2=2+3 returns 0. The TI-83 Plus performs the addition first because of EOS rules, and then it compares 4 to 5.

The expression 2+(2=2)+3 returns 6. The TI-83 Plus performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3.

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TEST LOGIC (Boolean) Operations

TEST LOGIC Menu

To display the TEST LOGIC menu, press y TEST ~.

This operator... Returns a 1 (true) if... TEST LOGIC

1: and Both values are nonzero (true). 2: or At least one value is nonzero (true). 3: xor Only one value is zero (false). 4: not( The value is zero (false).

Boolean Operators

Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero (false) or nonzero (true).

and, or, xor

and, or, and xor (exclusive or) return a value of 1 if an expression is true or 0 if an expression is false, according to the table below. valueA and valueB can be real numbers, expressions, or lists.

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valueA and valueB valueA or valueB valueA xor valueB

valueA valueB and or xor

0 0 returns 1 1 0

0 0 returns 0 1 1

0 0 returns 0 1 1

0 0 returns 0 0 0

not(

not( returns 1 if value (which can be an expression) is 0.

not(value)

Using Boolean Operations

Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C.

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Chapter 3: Function Graphing

Getting Started: Graphing a Circle

Getting Started is a fast-paced introduction. Read the chapter for details.

Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display and make the functions appear as a circle.

1. In Func mode, press o to display the Y= editor. Press y 100 to enter the expression Y=(100NX2), which defines the top half of the circle.

The expression Y=L(100NX2) defines the bottom half of the circle. On the TI-83 Plus, you can define one function in terms of another. To define Y2=LY1, press to enter the negation sign. Press ~ to display the VARS Y.VARS

menu. Then press to select 1:Function. The FUNCTION secondary menu is displayed. Press 1 to select 1:Y1.

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2. Press q 6 to select 6:ZStandard. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press .

Notice that the functions appear as an ellipse in the standard viewing window.

3. To adjust the display so that each pixel represents an equal width and height, press q 5 to select 5:ZSquare. The functions are replotted and now appear as a circle on the display.

4. To see the ZSquare window variables, press p and notice the new values for Xmin, Xmax, Ymin, and Ymax.

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Defining Graphs

TI-83 PlusGraphing Mode Similarities

Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-83 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing.

Defining a Graph

To define a graph in any graphing mode, follow these steps. Some steps are not always necessary.

1. Press z and set the appropriate graph mode.

2. Press o and enter, edit, or select one or more functions in the Y= editor.

3. Deselect stat plots, if necessary.

4. Set the graph style for each function.

5. Press p and define the viewing window variables.

6. Press y . and select the graph format settings.

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Displaying and Exploring a Graph

After you have defined a graph, press to display it. Explore the behavior of the function or functions using the TI-83 Plus tools described in this chapter.

Saving a Graph for Later Use

You can store the elements that define the current graph to any of 10 graph database variables (GDB1 through GDB9, and GDB0; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph.

These types of information are stored in a GDB.

Y= functions

Graph style settings

Window settings

Format settings

You can store a picture of the current graph display to any of 10 graph picture variables (Pic1 through Pic9, and Pic0; Chapter 8). Then you can superimpose one or more stored pictures onto the current graph.

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Setting the Graph Modes

Checking and Changing the Graphing Mode

To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select Func mode before you enter values for the window variables and before you enter the functions.

The TI-83 Plus has four graphing modes.

Func (function graphing)

Par (parametric graphing; Chapter 4)

Pol (polar graphing; Chapter 5)

Seq (sequence graphing; Chapter 6)

Other mode settings affect graphing results. Chapter 1 describes each mode setting.

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Float or 0123456789 (fixed) decimal mode affects displayed graph coordinates.

Radian or Degree angle mode affects interpretation of some functions.

Connected or Dot plotting mode affects plotting of selected functions.

Sequential or Simul graphing-order mode affects function plotting when more than one function is selected.

Setting Modes from a Program

To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps.

1. Press z to display the mode settings.

2. Press , ~, |, and } to place the cursor on the mode that you want to select.

3. Press to paste the mode name to the cursor location.

The mode is changed when the program is executed.

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Defining Functions

Displaying Functions in the Y= Editor

To display the Y= editor, press o. You can store up to 10 functions to the function variables Y1 through Y9, and Y0. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selected.

Defining or Editing a Function

To define or edit a function, follow these steps.

1. Press o to display the Y= editor.

2. Press to move the cursor to the function you want to define or edit. To erase a function, press .

3. Enter or edit the expression to define the function.

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You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.

The independent variable in the function is X. Func mode defines as X. To enter X, press or press [X].

When you enter the first character, the = is highlighted, indicating that the function is selected.

As you enter the expression, it is stored to the variable Yn as a user- defined function in the Y= editor.

4. Press or to move the cursor to the next function.

Defining a Function from the Home Screen or a Program

To define a function from the home screen or a program, begin on a blank line and follow these steps.

1. Press [], enter the expression, and then press [] again.

2. Press .

3. Press ~ 1 to select 1:Function from the VARS Y.VARS menu.

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4. Select the function name, which pastes the name to the cursor location on the home screen or program editor.

5. Press to complete the instruction.

"expression"!Yn

When the instruction is executed, the TI-83 Plus stores the expression to the designated variable Yn, selects the function, and displays the message Done.

Evaluating Y= Functions in Expressions

You can calculate the value of a Y= function Yn at a specified value of X. A list of values returns a list.

Yn(value) Yn({value1,value2,value3, . . .,value n})

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Selecting and Deselecting Functions

Selecting and Deselecting a Function

You can select and deselect (turn on and turn off) a function in the Y= editor. A function is selected when the = sign is highlighted. The TI-83 Plus graphs only the selected functions. You can select any or all functions Y1 through Y9, and Y0.

To select or deselect a function in the Y= editor, follow these steps.

1. Press o to display the Y= editor.

2. Move the cursor to the function you want to select or deselect.

3. Press | to place the cursor on the functions = sign.

4. Press to change the selection status.

When you enter or edit a function, it is selected automatically. When you clear a function, it is deselected.

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Turning On or Turning Off a Stat Plot in the Y= Editor

To view and change the on/off status of a stat plot in the Y= editor, use Plot1 Plot2 Plot3 (the top line of the Y= editor). When a plot is on, its name is highlighted on this line.

To change the on/off status of a stat plot from the Y= editor, press } and ~ to place the cursor on Plot1, Plot2, or Plot3, and then press .

Selecting and Deselecting Functions from the Home Screen or a Program

To select or deselect a function from the home screen or a program, begin on a blank line and follow these steps.

1. Press ~ to display the VARS Y.VARS menu.

2. Select 4:On/Off to display the ON/OFF secondary menu.

Plot1 is turned on. Plot2 and Plot3 are turned off.

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3. Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off one or more functions. The instruction you select is copied to the cursor location.

4. Enter the number (1 through 9, or 0; not the variable Yn) of each function you want to turn on or turn off.

If you enter two or more numbers, separate them with commas.

To turn on or turn off all functions, do not enter a number after FnOn or FnOff.

FnOn[function#,function#, . . .,function n] FnOff[function#,function#, . . .,function n]

5. Press . When the instruction is executed, the status of each function in the current mode is set and Done is displayed.

For example, in Func mode, FnOff :FnOn 1,3 turns off all functions in the Y= editor, and then turns on Y1 and Y3.

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Setting Graph Styles for Functions

Graph Style Icons in the Y= Editor

This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set Y1 as a solid line, Y2 as a dotted line, and Y3 as a thick line.

Icon Style Description

Line A solid line connects plotted points; this is the default in Connected mode

Thick A thick solid line connects plotted points

Above Shading covers the area above the graph

Below Shading covers the area below the graph

Path A circular cursor traces the leading edge of the graph and draws a path

Animate A circular cursor traces the leading edge of the graph without drawing a path

Dot A small dot represents each plotted point; this is the default in Dot mode

Note: Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes.

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Setting the Graph Style

To set the graph style for a function, follow these steps.

1. Press o to display the Y= editor.

2. Press and } to move the cursor to the function.

3. Press | | to move the cursor left, past the = sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.)

4. Press repeatedly to rotate through the graph styles. The seven styles rotate in the same order in which they are listed in the table above.

5. Press ~, }, or when you have selected a style.

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Shading Above and Below

When you select or for two or more functions, the TI-83 Plus rotates through four shading patterns.

Vertical lines shade the first function with a or graph style.

Horizontal lines shade the second.

Negatively sloping diagonal lines shade the third.

Positively sloping diagonal lines shade the fourth.

The rotation returns to vertical lines for the fifth or function, repeating the order described above.

When shaded areas intersect, the patterns overlap.

Note: When or is selected for a Y= function that graphs a family of curves, such as Y1={1,2,3}X, the four shading patterns rotate for each member of the family of curves.

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Setting a Graph Style from a Program

To set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu. To display this menu, press while in the program editor. function# is the number of the Y= function name in the current graphing mode. graphstyle# is an integer from 1 to 7 that corresponds to the graph style, as shown below.

1 = (line) 2 = (thick) 3 = (above) 4 = (below) 5 = (path) 6 = (animate) 7 = (dot)

GraphStyle(function#,graphstyle#)

For example, when this program is executed in Func mode, GraphStyle(1,3) sets Y1 to (above).

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Setting the Viewing Window Variables

The TI-83 Plus Viewing Window

The viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale) defines the distance between tick marks on the x-axis. Yscl (Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0.

Xmax

Ymin

Ymax

Xscl

Yscl

Xmin

Displaying the Window Variables

To display the current window variable values, press p. The window editor above and to the right shows the default values in Func graphing mode and Radian angle mode. The window variables differ from one graphing mode to another.

Xres sets pixel resolution (1 through 8) for function graphs only. The default is 1.

At Xres=1, functions are evaluated and graphed at each pixel on the x-axis.

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At Xres=8, functions are evaluated and graphed at every eighth pixel along the x-axis.

Tip: Small Xres values improve graph resolution but may cause the TI-83 Plus to draw graphs more slowly.

Changing a Window Variable Value

To change a window variable value from the window editor, follow these steps.

1. Press or } to move the cursor to the window variable you want to change.

2. Edit the value, which can be an expression.

Enter a new value, which clears the original value.

Move the cursor to a specific digit, and then edit it.

3. Press , , or }. If you entered an expression, the TI-83 Plus evaluates it. The new value is stored.

Note: Xmin<Xmax and Ymin<Ymax must be true in order to graph.

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Storing to a Window Variable from the Home Screen or a Program

To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps.

1. Enter the value you want to store.

2. Press .

3. Press to display the VARS menu.

4. Select 1:Window to display the Func window variables (X/Y secondary menu).

Press ~ to display the Par and Pol window variables (T/q

secondary menu).

Press ~ ~ to display the Seq window variables (U/V/W secondary menu).

5. Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location.

6. Press to complete the instruction.

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When the instruction is executed, the TI-83 Plus stores the value to the window variable and displays the value.

@X and @Y

The variables @X and @Y (items 8 and 9 on the VARS (1:Window) X/Y

secondary menu) define the distance from the center of one pixel to the center of any adjacent pixel on a graph (graphing accuracy). @X and @Y are calculated from Xmin, Xmax, Ymin, and Ymax when you display a graph.

@X = (Xmax N Xmin)

94 @Y = (Ymax N Ymin)

62

You can store values to @X and @Y. If you do, Xmax and Ymax are calculated from @X, Xmin, @Y, and Ymin.

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Setting the Graph Format

Displaying the Format Settings

To display the format settings, press y .. The default settings are highlighted below.

RectGC PolarGC Sets cursor coordinates. CoordOn CoordOff Sets coordinates display on or off. GridOff GridOn Sets grid off or on. AxesOn AxesOff Sets axes on or off. LabelOff LabelOn Sets axes label off or on. ExprOn ExprOff Sets expression display on or off.

Format settings define a graphs appearance on the display. Format settings apply to all graphing modes. Seq graphing mode has an additional mode setting (Chapter 6).

Changing a Format Setting

To change a format setting, follow these steps.

1. Press , ~, }, and | as necessary to move the cursor to the setting you want to select.

2. Press to select the highlighted setting.

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RectGC, PolarGC

RectGC (rectangular graphing coordinates) displays the cursor location as rectangular coordinates X and Y.

PolarGC (polar graphing coordinates) displays the cursor location as polar coordinates R and q.

The RectGC/PolarGC setting determines which variables are updated when you plot the graph, move the free-moving cursor, or trace.

RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed.

PolarGC updates X, Y, R, and q; if CoordOn format is selected, R and q are displayed.

CoordOn, CoordOff

CoordOn (coordinates on) displays the cursor coordinates at the bottom of the graph. If ExprOff format is selected, the function number is displayed in the top-right corner.

CoordOff (coordinates off) does not display the function number or coordinates.

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GridOff, GridOn

Grid points cover the viewing window in rows that correspond to the tick marks on each axis.

GridOff does not display grid points.

GridOn displays grid points.

AxesOn, AxesOff

AxesOn displays the axes.

AxesOff does not display the axes.

This overrides the LabelOff/LabelOn format setting.

LabelOff, LabelOn

LabelOff and LabelOn determine whether to display labels for the axes (X and Y), if AxesOn format is also selected.

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ExprOn, ExprOff

ExprOn and ExprOff determine whether to display the Y= expression when the trace cursor is active. This format setting also applies to stat plots.

When ExprOn is selected, the expression is displayed in the top-left corner of the graph screen.

When ExprOff and CoordOn both are selected, the number in the top-right corner specifies which function is being traced.

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Displaying Graphs

Displaying a New Graph

To display the graph of the selected function or functions, press . TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI-83 Plus plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated.

Pausing or Stopping a Graph

While plotting a graph, you can pause or stop graphing.

Press to pause; then press to resume.

Press to stop; then press to redraw.

Smart Graph

Smart Graph is a TI-83 Plus feature that redisplays the last graph immediately when you press , but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed.

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If you performed any of these actions since the graph was last displayed, the TI-83 Plus will replot the graph based on new values when you press s.

Changed a mode setting that affects graphs

Changed a function in the current picture

Selected or deselected a function or stat plot

Changed the value of a variable in a selected function

Changed a window variable or graph format setting

Cleared drawings by selecting ClrDraw

Changed a stat plot definition

Overlaying Functions on a Graph

On the TI-83 Plus, you can graph one or more new functions without replotting existing functions. For example, store sin(X) to Y1 in the Y= editor and press . Then store cos(X) to Y2 and press again. The function Y2 is graphed on top of Y1, the original function.

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Graphing a Family of Curves

If you enter a list (Chapter 11) as an element in an expression, the TI-83 Plus plots the function for each value in the list, thereby graphing a family of curves. In Simul graphing-order mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on.

{2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X).

{2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X).

Note: When using more than one list, the lists must have the same dimensions.

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Exploring Graphs with the Free-Moving Cursor

Free-Moving Cursor

When a graph is displayed, press |, ~, }, or to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or , the cursor moves from the center of the viewing window.

As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if CoordOn format is selected. The Float/Fix decimal mode setting determines the number of decimal digits displayed for the coordinate values.

To display the graph with no cursor and no coordinate values, press or . When you press |, ~, }, or , the cursor moves from the same position.

Graphing Accuracy

The free-moving cursor moves from pixel to pixel on the screen. When you move the cursor to a pixel that appears to be on the function, the cursor may be near, but not actually on, the function. The coordinate

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value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use r.

The coordinate values displayed as you move the cursor approximate actual math coordinates, *accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin, and Ymax get closer together (as in a Zoom In) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates.

Free- moving cursor on the curve

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Exploring Graphs with TRACE

Beginning a Trace

Use TRACE to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the Y= editor, at the middle X value on the screen. The cursor coordinates are displayed at the bottom of the screen if CoordOn format is selected. The Y= expression is displayed in the top-left corner of the screen, if ExprOn format is selected.

Moving the Trace Cursor

To move the TRACE cursor do this:

To the previous or next plotted point, press | or ~.

Five plotted points on a function (Xres affects this), press y | or y ~.

To any valid X value on a function, enter a value, and then press .

From one function to another, press } or .

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When the trace cursor moves along a function, the Y value is calculated from the X value; that is, Y=Yn(X). If the function is undefined at an X value, the Y value is blank.

If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

Moving the Trace Cursor from Function to Function

To move the trace cursor from function to function, press and }. The cursor follows the order of the selected functions in the Y= editor. The trace cursor moves to each function at the same X value. If ExprOn format is selected, the expression is updated.

Moving the Trace Cursor to Any Valid X Value

To move the trace cursor to any valid X value on the current function, enter the value. When you enter the first digit, an X= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the X= prompt. The value must

Trace cursor on the curve

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be valid for the current viewing window. When you have completed the entry, press to move the cursor.

Note: This feature does not apply to stat plots.

Panning to the Left or Right

If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right. Xmin and Xmax are updated to correspond to the new viewing window.

Quick Zoom

While tracing, you can press to adjust the viewing window so that the cursor location becomes the center of the new viewing window, even if the cursor is above or below the display. This allows panning up and down. After Quick Zoom, the cursor remains in TRACE.

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Leaving and Returning to TRACE

When you leave and return to TRACE, the trace cursor is displayed in the same location it was in when you left TRACE, unless Smart Graph has replotted the graph.

Using TRACE in a Program

On a blank line in the program editor, press r. The instruction Trace is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press to resume program execution.

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Exploring Graphs with the ZOOM Instructions

ZOOM Menu

To display the ZOOM menu, press q. You can adjust the viewing window of the graph quickly in several ways. All ZOOM instructions are accessible from programs.

ZOOM MEMORY

1:ZBox Draws a box to define the viewing window. 2:Zoom In Magnifies the graph around the cursor. 3:Zoom Out Views more of a graph around the cursor. 4:ZDecimal Sets @X and @Y to 0.1. 5:ZSquare Sets equal-size pixels on the X and Y axes. 6:ZStandard Sets the standard window variables. 7:ZTrig Sets the built-in trig window variables. 8:ZInteger Sets integer values on the X and Y axes. 9:ZoomStat Sets the values for current stat lists. 0:ZoomFit Fits YMin and YMax between XMin and XMax.

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Zoom Cursor

When you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the graph becomes the zoom cursor (+), a smaller version of the free-moving cursor (+).

ZBox

To define a new viewing window using ZBox, follow these steps.

1. Select 1:ZBox from the ZOOM menu. The zoom cursor is displayed at the center of the screen.

2. Move the zoom cursor to any spot you want to define as a corner of the box, and then press . When you move the cursor away from the first defined corner, a small, square dot indicates the spot.

3. Press |, }, ~, or . As you move the cursor, the sides of the box lengthen or shorten proportionately on the screen.

Note: To cancel ZBox before you press , press .

4. When you have defined the box, press to replot the graph.

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To use ZBox to define another box within the new graph, repeat steps 2 through 4. To cancel ZBox, press .

Zoom In, Zoom Out

Zoom In magnifies the part of the graph that surrounds the cursor location. Zoom Out displays a greater portion of the graph, centered on the cursor location. The XFact and YFact settings determine the extent of the zoom.

To zoom in on a graph, follow these steps.

1. Check XFact and YFact; change as needed.

2. Select 2:Zoom In from the ZOOM menu. The zoom cursor is displayed.

3. Move the zoom cursor to the point that is to be the center of the new viewing window.

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4. Press . The TI-83 Plus adjusts the viewing window by XFact and YFact; updates the window variables; and replots the selected functions, centered on the cursor location.

5. Zoom in on the graph again in either of two ways.

To zoom in at the same point, press .

To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press .

To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5.

To cancel Zoom In or Zoom Out, press .

ZDecimal

ZDecimal replots the functions immediately. It updates the window variables to preset values, as shown below. These values set @X and @Y equal to 0.1 and set the X and Y value of each pixel to one decimal place.

Xmin=L4.7 Ymin=L3.1 Xmax=4.7 Ymax=3.1 Xscl=1 Yscl=1

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ZSquare

ZSquare replots the functions immediately. It redefines the viewing window based on the current values of the window variables. It adjusts in only one direction so that @X=@Y, which makes the graph of a circle look like a circle. Xscl and Yscl remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph.

ZStandard

ZStandard replots the functions immediately. It updates the window variables to the standard values shown below.

Xmin=L10 Ymin=L10 Xres=1 Xmax=10 Ymax=10 Xscl=1 Yscl=1

ZTrig

ZTrig replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in Radian mode are shown below.

Xmin=L(4724)p Ymin=L4 Xmax=(4724)p Ymax=4 Xscl=p/2 Yscl=1

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ZInteger

ZInteger redefines the viewing window to the dimensions shown below. To use ZInteger, move the cursor to the point that you want to be the center of the new window, and then press ; ZInteger replots the functions.

@X=1 Xscl=10 @Y=1 Yscl=10

ZoomStat

ZoomStat redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only Xmin and Xmax are adjusted.

ZoomFit

ZoomFit replots the functions immediately. ZoomFit recalculates YMin and YMax to include the minimum and maximum Y values of the selected functions between the current XMin and XMax. XMin and XMax are not changed.

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Using ZOOM MEMORY

ZOOM MEMORY Menu

To display the ZOOM MEMORY menu, press q ~.

ZOOM MEMORY

1: ZPrevious Uses the previous viewing window. 2: ZoomSto Stores the user-defined window. 3: ZoomRcl Recalls the user-defined window. 4: SetFactors... Changes Zoom In and Zoom Out factors.

ZPrevious

ZPrevious replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction.

ZoomSto

ZoomSto immediately stores the current viewing window. The graph is displayed, and the values of the current window variables are stored in the user-defined ZOOM variables ZXmin, ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and ZXres.

These variables apply to all graphing modes. For example, changing the value of ZXmin in Func mode also changes it in Par mode.

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ZoomRcl

ZoomRcl graphs the selected functions in a user-defined viewing window. The user-defined viewing window is determined by the values stored with the ZoomSto instruction. The window variables are updated with the user-defined values, and the graph is plotted.

ZOOM FACTORS

The zoom factors, XFact and YFact, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to Zoom In or Zoom Out around a point.

Checking XFact and YFact

To display the ZOOM FACTORS screen, where you can review the current values for XFact and YFact, select 4:SetFactors from the ZOOM MEMORY

menu. The values shown are the defaults.

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Changing XFact and YFact

You can change XFact and YFact in either of two ways.

Enter a new value. The original value is cleared automatically when you enter the first digit.

Place the cursor on the digit you want to change, and then enter a value or press { to delete it.

Using ZOOM MEMORY Menu Items from the Home Screen or a Program

From the home screen or a program, you can store directly to any of the user-defined ZOOM variables.

From a program, you can select the ZoomSto and ZoomRcl instructions from the ZOOM MEMORY menu.

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Using the CALC (Calculate) Operations

CALCULATE Menu

To display the CALCULATE menu, press y CALC. Use the items on this menu to analyze the current graph functions.

CALCULATE 1:value Calculates a function Y value for a given X. 2:zero Finds a zero (x-intercept) of a function. 3:minimum Finds a minimum of a function. 4:maximum Finds a maximum of a function. 5:intersect Finds an intersection of two functions. 6:dy/dx Finds a numeric derivative of a function. 7:f(x)dx Finds a numeric integral of a function.

value

value evaluates one or more currently selected functions for a specified value of X.

Note: When a value is displayed for X, press to clear the value. When no value is displayed, press to cancel the value operation.

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To evaluate a selected function at X, follow these steps.

1. Select 1:value from the CALCULATE menu. The graph is displayed with X= in the bottom-left corner.

2. Enter a real value, which can be an expression, for X between Xmin and Xmax.

3. Press .

The cursor is on the first selected function in the Y= editor at the X value you entered, and the coordinates are displayed, even if CoordOff format is selected.

To move the cursor from function to function at the entered X value, press } or . To restore the free-moving cursor, press | or ~.

zero

zero finds a zero (x-intercept or root) of a function using solve(. Functions can have more than one x-intercept value; zero finds the zero closest to your guess.

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The time zero spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess.

To find a zero of a function, follow these steps.

1. Select 2:zero from the CALCULATE menu. The current graph is displayed with Left Bound? in the bottom-left corner.

2. Press } or to move the cursor onto the function for which you want to find a zero.

3. Press | or ~ (or enter a value) to select the x-value for the left bound of the interval, and then press . A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner. Press | or ~ (or enter a value) to select the x-value for the right bound, and then press . A 3 indicator on the graph screen shows the right bound. Guess? is then displayed in the bottom-left corner.

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4. Press | or ~ (or enter a value) to select a point near the zero of the function, between the bounds, and then press .

The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~.

minimum, maximum

minimum and maximum find a minimum or maximum of a function within a specified interval to a tolerance of 1L5.

To find a minimum or maximum, follow these steps.

1. Select 3:minimum or 4:maximum from the CALCULATE menu. The current graph is displayed.

2. Select the function and set left bound, right bound, and guess as described for zero.

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The cursor is on the solution, and the coordinates are displayed, even if you have selected CoordOff format; Minimum or Maximum is displayed in the bottom-left corner.

To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~.

intersect

intersect finds the coordinates of a point at which two or more functions intersect using solve(. The intersection must appear on the display to use intersect.

To find an intersection, follow these steps.

1. Select 5:intersect from the CALCULATE menu. The current graph is displayed with First curve? in the bottom-left corner.

2. Press or }, if necessary, to move the cursor to the first function, and then press . Second curve? is displayed in the bottom-left corner.

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3. Press or }, if necessary, to move the cursor to the second function, and then press .

4. Press ~ or | to move the cursor to the point that is your guess as to location of the intersection, and then press .

The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. Intersection is displayed in the bottom-left corner. To restore the free-moving cursor, press |, }, ~, or .

dy/dx

dy/dx (numerical derivative) finds the numerical derivative (slope) of a function at a point, with H=1L3.

To find a functions slope at a point, follow these steps.

1. Select 6:dy/dx from the CALCULATE menu. The current graph is displayed.

2. Press } or to select the function for which you want to find the numerical derivative.

3. Press | or ~ (or enter a value) to select the X value at which to calculate the derivative, and then press .

The cursor is on the solution and the numerical derivative is displayed.

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To move to the same x-value for other selected functions, press } or . To restore the free-moving cursor, press | or ~.

f(x)dx

f(x)dx (numerical integral) finds the numerical integral of a function in a specified interval. It uses the fnInt( function, with a tolerance of H=1L3.

To find the numerical derivative of a function, follow these steps.

1. Select 7:f(x)dx from the CALCULATE menu. The current graph is displayed with Lower Limit? in the bottom-left corner.

2. Press } or to move the cursor to the function for which you want to calculate the integral.

3. Set lower and upper limits as you would set left and right bounds for zero. The integral value is displayed, and the integrated area is shaded.

Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area.

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Chapter 4: Parametric Graphing

Getting Started: Path of a Ball

Getting Started is a fast-paced introduction. Read the chapter for details.

Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.

For initial velocity v0 and angle q, the position of the ball as a function of time has horizontal and vertical components.

Horizontal: X1(t)=tv0cos(q) Vertical: Y1(t)=tv0sin(q)N 1 2 gt2

The vertical and horizontal vectors of the balls motion also will be graphed.

Vertical vector: X2(t)=0 Y2(t)=Y1(t) Horizontal vector: X3(t)=X1(t) Y3(t)=0 Gravity constant: g=9.8 m/sec2

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1. Press z. Press ~ to select Par mode. Press ~ to select Simul for simultaneous graphing of all three parametric equations in this example.

2. Press o. Press 30 25 y ; 1 (to select ) to define X1T in terms of T.

3. Press 30 25 y ; 1 9.8 2 to define Y1T.

The vertical component vector is defined by X2T

and Y2T.

4. Press 0 to define X2T.

5. Press ~ to display the VARS Y.VARS menu. Press 2 to display the PARAMETRIC secondary menu. Press 2 to define Y2T.

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The horizontal component vector is defined by X3T and Y3T.

6. Press ~ 2, and then press 1 to define X3T. Press 0 to define Y3T.

7. Press | | } to change the graph style to for X3T and Y3T. Press } to change the graph style to for X2T and Y2T. Press } to change the graph style to for X1T and Y1T. (These keystrokes assume that all graph styles were set to originally.)

8. Press p. Enter these values for the window variables.

Tmin=0 Xmin=L10 Ymin=L5 Tmax=5 Xmax=100 Ymax=15 Tstep=.1 Xscl=50 Yscl=10

9. Press y . ~ to set AxesOff, which turns off the axes.

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10.Press . The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion.

Tip: To simulate the ball flying through the air, set graph style to (animate) for X1T and Y1T.

11.Press r to obtain numerical results and answer the questions at the beginning of this section.

Tracing begins at Tmin on the first parametric equation (X1T and Y1T). As you press ~ to trace the curve, the cursor follows the path of the ball over time. The values for X (distance), Y (height), and T (time) are displayed at the bottom of the screen.

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Defining and Displaying Parametric Graphs

TI-83 Plus Graphing Mode Similarities

The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing.

Setting Parametric Graphing Mode

To display the mode screen, press z. To graph parametric equations, you must select Par graphing mode before you enter window variables and before you enter the components of parametric equations.

Displaying the Parametric Y= Editor

After selecting Par graphing mode, press o to display the parametric Y= editor.

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In this editor, you can display and enter both the X and Y components of up to six equations, X1T and Y1T through X6T and Y6T. Each is defined in terms of the independent variable T. A common application of parametric graphs is graphing equations over time.

Selecting a Graph Style

The icons to the left of X1T through X6T represent the graph style of each parametric equation (Chapter 3). The default in Par mode is (line), which connects plotted points. Line, (thick), (path), (animate), and (dot) styles are available for parametric graphing.

Defining and Editing Parametric Equations

To define or edit a parametric equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is T. In Par graphing mode, you can enter the parametric variable T in either of two ways.

Press .

Press T.

Two components, X and Y, define a single parametric equation. You must define both of them.

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Selecting and Deselecting Parametric Equations

The TI-83 Plus graphs only the selected parametric equations. In the Y= editor, a parametric equation is selected when the = signs of both the X and Y components are highlighted. You may select any or all of the equations X1T and Y1T through X6T and Y6T.

To change the selection status, move the cursor onto the = sign of either the X or Y component and press . The status of both the X and Y components is changed.

Setting Window Variables

To display the window variable values, press p. These variables define the viewing window. The values below are defaults for Par graphing in Radian angle mode.

Tmin=0 Smallest T value to evaluate Tmax=6.2831853... Largest T value to evaluate (2p) Tstep=.1308996... T value increment (p24) Xmin=L10 Smallest X value to be displayed Xmax=10 Largest X value to be displayed Xscl=1 Spacing between the X tick marks Ymin=L10 Smallest Y value to be displayed Ymax=10 Largest Y value to be displayed Yscl=1 Spacing between the Y tick marks

Note: To ensure that sufficient points are plotted, you may want to change the T window variables.

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Setting the Graph Format

To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings; Seq graphing mode has an additional axes format setting.

Displaying a Graph

When you press , the TI-83 Plus plots the selected parametric equations. It evaluates the X and Y components for each value of T (from Tmin to Tmax in intervals of Tstep), and then plots each point defined by X and Y. The window variables define the viewing window.

As the graph is plotted, X, Y, and T are updated.

Smart Graph applies to parametric graphs (Chapter 3).

Window Variables and Y.VARS Menus

You can perform these actions from the home screen or a program.

Access functions by using the name of the X or Y component of the equation as a variable.

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Store parametric equations.

Select or deselect parametric equations.

Store values directly to window variables.

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Exploring Parametric Graphs

Free-Moving Cursor

The free-moving cursor in Par graphing works the same as in Func graphing.

In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed.

In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed.

TRACE

To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one Tstep at a time. When you begin a trace, the trace cursor is on the first selected function at Tmin. If ExprOn is selected, then the function is displayed.

In RectGC format, TRACE updates and displays the values of X, Y, and T if CoordOn format is on.

In PolarGC format, X, Y, R, q and T are updated; if CoordOn format is selected, R, q, and T are displayed. The X and Y (or R and q) values are calculated from T.

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To move five plotted points at a time on a function, press y | or y ~. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.

Quick Zoom is available in Par graphing; panning is not (Chapter 3).

Moving the Trace Cursor to Any Valid T Value

To move the trace cursor to any valid T value on the current function, enter the number. When you enter the first digit, a T= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the T= prompt. The value must be valid for the current viewing window. When you have completed the entry, press to move the cursor.

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ZOOM

ZOOM operations in Par graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.

The T window variables (Tmin, Tmax, and Tstep) are only affected when you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items 1:ZTmin, 2:ZTmax, and 3:ZTstep are the zoom memory variables for Par graphing.

CALC

CALC operations in Par graphing work the same as in Func graphing. The CALCULATE menu items available in Par graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt.

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Chapter 5: Polar Graphing

Getting Started: Polar Rose

Getting Started is a fast-paced introduction. Read the chapter for details.

The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B.

1. Press z to display the mode screen. Press ~ ~ to select Pol graphing mode. Select the defaults (the options on the left) for the other mode settings.

2. Press o to display the polar Y= editor. Press 8 2.5 to define r1.

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3. Press q 6 to select 6:ZStandard and graph the equation in the standard viewing window. The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets qmax=2p and defines the window, rather than the pixels, as square.

4. Press p to display the window variables. Press 4 y B to increase the value of qmax to 4p.

5. Press q 5 to select 5:ZSquare and plot the graph.

6. Repeat steps 2 through 5 with new values for the variables A and B in the polar equation r1=Asin(Bq). Observe how the new values affect the graph.

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Defining and Displaying Polar Graphs

TI-83 Plus Graphing Mode Similarities

The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing.

Setting Polar Graphing Mode

To display the mode screen, press z. To graph polar equations, you must select Pol graphing mode before you enter values for the window variables and before you enter polar equations.

Displaying the Polar Y= Editor

After selecting Pol graphing mode, press o to display the polar Y= editor.

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In this editor, you can enter and display up to six polar equations, r1

through r6. Each is defined in terms of the independent variable q.

Selecting Graph Styles

The icons to the left of r1 through r6 represent the graph style of each polar equation (Chapter 3). The default in Pol graphing mode is (line), which connects plotted points. Line, (thick), (path), (animate), and (dot) styles are available for polar graphing.

Defining and Editing Polar Equations

To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is q. In Pol graphing mode, you can enter the polar variable q in either of two ways.

Press .

Press q.

Selecting and Deselecting Polar Equations

The TI-83 Plus graphs only the selected polar equations. In the Y= editor, a polar equation is selected when the = sign is highlighted. You may select any or all of the equations.

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To change the selection status, move the cursor onto the = sign, and then press .

Setting Window Variables

To display the window variable values, press p. These variables define the viewing window. The values below are defaults for Pol graphing in Radian angle mode.

qmin=0 Smallest q value to evaluate qmax=6.2831853... Largest q value to evaluate (2p) qstep=.1308996... Increment between q values (p24) Xmin=L10 Smallest X value to be displayed Xmax=10 Largest X value to be displayed Xscl=1 Spacing between the X tick marks Ymin=L10 Smallest Y value to be displayed Ymax=10 Largest Y value to be displayed Yscl=1 Spacing between the Y tick marks

Note: To ensure that sufficient points are plotted, you may want to change the q window variables.

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Setting the Graph Format

To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings.

Displaying a Graph

When you press , the TI-83 Plus plots the selected polar equations. It evaluates R for each value of q (from qmin to qmax in intervals of qstep) and then plots each point. The window variables define the viewing window.

As the graph is plotted, X, Y, R, and q are updated.

Smart Graph applies to polar graphs (Chapter 3).

Window Variables and Y.VARS Menus

You can perform these actions from the home screen or a program.

Access functions by using the name of the equation as a variable.

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Store polar equations.

Select or deselect polar equations.

Store values directly to window variables.

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Exploring Polar Graphs

Free-Moving Cursor

The free-moving cursor in Pol graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed.

TRACE

To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one qstep at a time. When you begin a trace, the trace cursor is on the first selected function at qmin. If ExprOn format is selected, then the equation is displayed.

In RectGC format, TRACE updates the values of X, Y, and q; if CoordOn format is selected, X, Y, and q are displayed. In PolarGC format, TRACE

updates X, Y, R, and q; if CoordOn format is selected, R and q are displayed.

To move five plotted points at a time on a function, press y | or y ~. If you move the trace cursor beyond the top or bottom of the

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screen, the coordinate values at the bottom of the screen continue to change appropriately.

Quick Zoom is available in Pol graphing mode; panning is not (Chapter 3).

Moving the Trace Cursor to Any Valid q Value

To move the trace cursor to any valid q value on the current function, enter the number. When you enter the first digit, a q= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the q= prompt. The value must be valid for the current viewing window. When you complete the entry, press to move the cursor.

ZOOM

ZOOM operations in Pol graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.

The q window variables (qmin, qmax, and qstep) are not affected, except when you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items 4:Zqmin, 5:Zqmax, and 6:Zqstep are zoom memory variables for Pol graphing.

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CALC

CALC operations in Pol graphing work the same as in Func graphing. The CALCULATE menu items available in Pol graphing are 1:value, 2:dy/dx, and 3:dr/dq.

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Chapter 6: Sequence Graphing

Getting Started: Forest and Trees

Getting Started is a fast-paced introduction. Read the chapter for details.

A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees?

1. Press z. Press ~ ~ ~ to select Seq graphing mode.

2. Press y . and select Time axes format and ExprOn format if necessary.

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3. Press o. If the graph-style icon is not (dot), press | |, press until is displayed, and then press ~ ~.

4. Press ~ 3 to select iPart( (integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain.

Press 8 y [u] 1 to define the number of trees after each harvest. Press 1000 to define the new trees. Press 4000 to define the number of trees at the beginning of the program.

5. Press p 0 to set nMin=0. Press 50 to set nMax=50. nMin and nMax evaluate forest size over 50 years. Set the other window variables.

PlotStart=1 Xmin=0 Ymin=0 PlotStep=1 Xmax=50 Ymax=6000

Xscl=10 Yscl=1000

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6. Press r. Tracing begins at nMin (the start of the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for n (number of years), X (X=n, because n is plotted on the x-axis), and Y (tree count) are displayed at the bottom. When will the forest stabilize? With how many trees?

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Defining and Displaying Sequence Graphs

TI-83 Plus Graphing Mode Similarities

The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing.

Setting Sequence Graphing Mode

To display the mode screen, press z. To graph sequence functions, you must select Seq graphing mode before you enter window variables and before you enter sequence functions.

Sequence graphs automatically plot in Simul mode, regardless of the current plotting-order mode setting.

TI-83 Plus Sequence Functions u, v, and w

The TI-83 Plus has three sequence functions that you can enter from the keyboard: u, v, and w. They are above the , , and keys.

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You can define sequence functions in terms of:

The independent variable n

The previous term in the sequence function, such as u(nN1)

The term that precedes the previous term in the sequence function, such as u(nN2)

The previous term or the term that precedes the previous term in another sequence function, such as u(nN1) or u(nN2) referenced in the sequence v(n).

Note: Statements in this chapter about u(n) are also true for v(n) and w(n); statements about u(nN1) are also true for v(nN1) and w(nN1); statements about u(nN2) are also true for v(nN2) and w(nN2).

Displaying the Sequence Y= Editor

After selecting Seq mode, press o to display the sequence Y= editor.

In this editor, you can display and enter sequences for u(n), v(n), and w(n). Also, you can edit the value for nMin, which is the sequence window variable that defines the minimum n value to evaluate.

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The sequence Y= editor displays the nMin value because of its relevance to u(nMin), v(nMin), and w(nMin), which are the initial values for the sequence equations u(n), v(n), and w(n), respectively.

nMin in the Y= editor is the same as nMin in the window editor. If you enter a new value for nMin in one editor, the new value for nMin is updated in both editors.

Note: Use u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which requires an initial value.

Selecting Graph Styles

The icons to the left of u(n), v(n), and w(n) represent the graph style of each sequence (Chapter 3). The default in Seq mode is (dot), which shows discrete values. Dot, (line), and (thick) styles are available for sequence graphing. Graph styles are ignored in Web format.

Selecting and Deselecting Sequence Functions

The TI-83 Plus graphs only the selected sequence functions. In the Y= editor, a sequence function is selected when the = signs of both u(n)= and u(nMin)= are highlighted.

To change the selection status of a sequence function, move the cursor onto the = sign of the function name, and then press . The status is changed for both the sequence function u(n) and its initial value u(nMin).

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Defining and Editing a Sequence Function

To define or edit a sequence function, follow the steps in Chapter 3 for defining a function. The independent variable in a sequence is n.

In Seq graphing mode, you can enter the sequence variable in either of two ways.

Press .

Press y N [N].

You can enter the function name from the keyboard.

To enter the function name u, press y [u] (above ).

To enter the function name v, press y [v] (above ).

To enter the function name w, press y [w] (above ).

Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values. n is always a series of consecutive integers, starting at zero or any positive integer.

Nonrecursive Sequences

In a nonrecursive sequence, the nth term is a function of the independent variable n. Each term is independent of all other terms.

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For example, in the nonrecursive sequence below, you can calculate u(5) directly, without first calculating u(1) or any previous term.

The sequence equation above returns the sequence 2, 4, 6, 8, 10, for n = 1, 2, 3, 4, 5, .

Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences.

Recursive Sequences

In a recursive sequence, the nth term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by u(nN1) and u(nN2). A recursive sequence may also be defined in relation to n, as in u(n)=u(nN1)+n.

For example, in the sequence below you cannot calculate u(5) without first calculating u(1), u(2), u(3), and u(4).

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Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, . . .

Tip: On the TI-83 Plus, you must type each character of the terms. For example, to enter u(nN1), press y [u] .

Recursive sequences require an initial value or values, since they reference undefined terms.

If each term in the sequence is defined in relation to the previous term, as in u(nN1), you must specify an initial value for the first term.

If each term in the sequence is defined in relation to the term that precedes the previous term, as in u(nN2), you must specify initial values for the first two terms. Enter the initial values as a list enclosed in braces ({ }) with commas separating the values.

The value of the first term is 0 and the value of the second term is 1 for the sequence u(n).

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Setting Window Variables

To display the window variables, press p. These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle modes.

nMin=1 Smallest n value to evaluate nMax=10 Largest n value to evaluate PlotStart=1 First term number to be plotted PlotStep=1 Incremental n value (for graphing only) Xmin=L10 Smallest X value to be displayed Xmax=10 Largest X value to be displayed Xscl=1 Spacing between the X tick marks Ymin=L10 Smallest Y value to be displayed Ymax=10 Largest Y value to be displayed Yscl=1 Spacing between the Y tick marks

nMin must be an integer 0. nMax, PlotStart, and PlotStep must be integers 1.

nMin is the smallest n value to evaluate. nMin also is displayed in the sequence Y= editor. nMax is the largest n value to evaluate. Sequences are evaluated at u(nMin), u(nMin+1), u(nMin+2) , . . . , u(nMax).

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PlotStart is the first term to be plotted. PlotStart=1 begins plotting on the first term in the sequence. If you want plotting to begin with the fifth term in a sequence, for example, set PlotStart=5. The first four terms are evaluated but are not plotted on the graph.

PlotStep is the incremental n value for graphing only. PlotStep does not affect sequence evaluation; it only designates which points are plotted on the graph. If you specify PlotStep=2, the sequence is evaluated at each consecutive integer, but it is plotted on the graph only at every other integer.

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Selecting Axes Combinations

Setting the Graph Format

To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode.

Time Webuv vw uw Type of sequence plot (axes) RectGC PolarGC Rectangular or polar output CoordOn CoordOff Cursor coordinate display on/off GridOff GridOn Grid display off or on AxesOn AxesOff Axes display on or off LabelOff LabelOn Axes label display off or on ExprOn ExprOff Expression display on or off

Setting Axes Format

For sequence graphing, you can select from five axes formats. The table below shows the values that are plotted on the x-axis and y-axis for each axes setting.

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Axes Setting x-axis y-axis

Time n u(n), v(n), w(n)

Web u(nN1), v(nN1), w(nN1) u(n), v(n), w(n)

uv u(n) v(n)

vw v(n) w(n)

uw u(n) w(n)

Displaying a Sequence Graph

To plot the selected sequence functions, press . As a graph is plotted, the TI-83 Plus updates X, Y, and n.

Smart Graph applies to sequence graphs (Chapter 3).

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Exploring Sequence Graphs

Free-Moving Cursor

The free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed.

TRACE

The axes format setting affects TRACE.

When Time, uv, vw, or uw axes format is selected, TRACE moves the cursor along the sequence one PlotStep increment at a time. To move five plotted points at once, press y ~ or y |.

When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by PlotStart, even if it is outside the viewing window.

Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, press . The trace cursor returns to nMin.

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In Web format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the initial value of the first selected function.

Tip: To move the cursor to a specified n during a trace, enter a value for n, and press . For example, to quickly return the cursor to the beginning of the sequence, paste nMin to the n= prompt and press .

Moving the Trace Cursor to Any Valid n Value

To move the trace cursor to any valid n value on the current function, enter the number. When you enter the first digit, an n = prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the n = prompt. The value must be valid for the current viewing window. When you have completed the entry, press to move the cursor.

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ZOOM

ZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.

PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The VARS Zoom secondary menu ZU items 1 through 7 are the ZOOM MEMORY variables for Seq graphing.

CALC

The only CALC operation available in Seq graphing is value.

When Time axes format is selected, value displays Y (the u(n) value) for a specified n value.

When Web axes format is selected, value draws the web and displays Y (the u(n) value) for a specified n value.

When uv, vw, or uw axes format is selected, value displays X and Y according to the axes format setting. For example, for uv axes format, X represents u(n) and Y represents v(n).

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Evaluating u, v, and w

To enter the sequence names u, v, or w, press y [u], [v], or [w]. You can evaluate these names in any of three ways.

Calculate the nth value in a sequence.

Calculate a list of values in a sequence.

Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional; default is 1.

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Graphing Web Plots

Graphing a Web Plot

To select Web axes format, press y . ~ . A web plot graphs u(n) versus u(nN1), which you can use to study long-term behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes.

Valid Functions for Web Plots

When Web axes format is selected, a sequence will not graph properly or will generate an error.

It must be recursive with only one recursion level (u(nN1) but not u(nN2)).

It cannot reference n directly.

It cannot reference any defined sequence except itself.

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Displaying the Graph Screen

In Web format, press to display the graph screen. The TI-83 Plus:

Draws a y=x reference line in AxesOn format.

Plots the selected sequences with u(nN1) as the independent variable.

Note: A potential convergence point occurs whenever a sequence intersects the y=x reference line. However, the sequence may or may not actually converge at that point, depending on the sequences initial value.

Drawing the Web

To activate the trace cursor, press r. The screen displays the sequence and the current n, X, and Y values (X represents u(nN1) and Y represents u(n)). Press ~ repeatedly to draw the web step by step, starting at nMin. In Web format, the trace cursor follows this course.

1. It starts on the x-axis at the initial value u(nMin) (when PlotStart=1).

2. It moves vertically (up or down) to the sequence.

3. It moves horizontally to the y=x reference line.

4. It repeats this vertical and horizontal movement as you continue to press ~.

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Using Web Plots to Illustrate Convergence

Example: Convergence

1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is set to (dot), and then define nMin, u(n) and u(nMin) as shown below.

2. Press y . to set Time axes format.

3. Press p and set the variables as shown below. nMin=1 Xmin=0 Ymin=L10 nMax=25 Xmax=25 Ymax=10 PlotStart=1 Xscl=1 Yscl=1 PlotStep=1

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4. Press to graph the sequence.

5. Press y . and select the Web axes setting.

6. Press p and change the variables below. Xmin=L10 Xmax=10

7. Press to graph the sequence.

8. Press r, and then press ~ to draw the web. The displayed cursor coordinates n, X (u(nN1)), and Y (u(n)) change accordingly. When you press ~, a new n value is displayed, and the trace cursor is on the sequence. When you press ~ again, the n value remains the same, and the cursor moves to the y=x reference line. This pattern repeats as you trace the web.

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Graphing Phase Plots

Graphing with uv, vw, and uw

The phase-plot axes settings uv, vw, and uw show relationships between two sequences. To select a phase-plot axes setting, press y ., press ~ until the cursor is on uv, vw, or uw, and then press .

Axes Setting x-axis y-axis

uv u(n) v(n)

vw v(n) w(n)

uw u(n) w(n)

Example: Predator-Prey Model

Use the predator-prey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.

This example uses the model to determine the equilibrium populations of foxes and rabbits, with initial populations of 200 rabbits (u(nMin)) and 50 foxes (v(nMin)).

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These are the variables (given values are in parentheses):

R = number of rabbits M = rabbit population growth rate without foxes (.05) K = rabbit population death rate with foxes (.001) W = number of foxes G = fox population growth rate with rabbits (.0002) D = fox population death rate without rabbits (.03) n = time (in months) Rn = RnN1(1+MNKWnN1) Wn = WnN1(1+GRnN1ND)

1. Press o in Seq mode to display the sequence Y= editor. Define the sequences and initial values for Rn and Wn as shown below. Enter the sequence Rn as u(n) and enter the sequence Wn as v(n).

2. Press y . to select Time axes format.

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3. Press p and set the variables as shown below. nMin=0 Xmin=0 Ymin=0 nMax=400 Xmax=400 Ymax=300 PlotStart=1 Xscl=100 Yscl=100 PlotStep=1

4. Press to graph the sequence.

5. Press r ~ to individually trace the number of rabbits (u(n)) and foxes (v(n)) over time (n).

Tip: Press a number, and then press to jump to a specific n value (month) while in TRACE.

6. Press y . ~ ~ to select uv axes format.

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7. Press p and change these variables as shown below. Xmin=84 Ymin=25 Xmax=237 Ymax=75 Xscl=50 Yscl=10

8. Press r. Trace both the number of rabbits (X) and the number of foxes (Y) through 400 generations.

Note: When you press r, the equation for u is displayed in the top-left corner. Press } or to see the equation for v.

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Comparing TI-83 Plus and TI-82 Sequence Variables

Sequences and Window Variables

Refer to the table if you are familiar with the TI-82. It shows TI-83 Plus sequences and sequence window variables, as well as their TI-82 counterparts.

TI-83 Plus TI.82

In the Y= editor:

u(n) Un

u(nMin) UnStart (window variable)

v(n) Vn

v(nMin) VnStart (window variable)

w(n) not available

w(nMin) not available

In the window editor:

nMin nStart

nMax nMax

PlotStart nMin

PlotStep not available

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Keystroke Differences Between TI-83 Plus and TI-82

Sequence Keystroke Changes

Refer to the table if you are familiar with the TI-82. It compares TI-83 Plus sequence-name syntax and variable syntax with TI.82 sequence-name syntax and variable syntax.

TI-83 Plus / TI-82 On TI-83 Plus, press: On TI-82, press:

n / n y [n]

u(n) / Un y [u]

y

v(n) / Vn y [v]

y

w(n) y [w]

not available

u(nN1) / UnN1 y [u]

y

v(nN1) / VnN1 y [v]

y

w(nN1) y [w]

not available

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Chapter 7: Tables

Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details.

Evaluate the function Y = X3 N 2X at each integer between L10 and 10. How many sign changes occur, and at what X values?

1. Press z to set Func graphing mode.

2. Press o. Press 3 to select 3. Then press 2 to enter the function Y1=X3N2X.

3. Press y - to display the TABLE SETUP

screen. Press 10 to set TblStart=L10. Press 1 to set @Tbl=1.

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Press to select Indpnt: Auto (automatically generated independent values). Press to select Depend: Auto (automatically generated dependent values).

4. Press y 0 to display the table screen.

5. Press until you see the sign changes in the value of Y1. How many sign changes occur, and at what X values?

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Setting Up the Table

TABLE SETUP Screen

To display the TABLE SETUP screen, press y -.

TblStart, @Tbl

TblStart (table start) defines the initial value for the independent variable. TblStart applies only when the independent variable is generated automatically (when Indpnt: Auto is selected).

@Tbl (table step) defines the increment for the independent variable.

Note: In Seq mode, both TblStart and @Tbl must be integers.

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Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask

Selections Table Characteristics

Indpnt: Auto Depend: Auto

Values are displayed automatically in both the independent-variable column and in all dependent- variable columns.

Indpnt: Ask Depend: Auto

The table is empty; when you enter a value for the independent variable, all corresponding dependent- variable values are calculated and displayed automatically.

Indpnt: Auto Depend: Ask

Values are displayed automatically for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press .

Indpnt: Ask Depend: Ask

The table is empty; enter values for the independent variable; to generate a value for a dependent variable, move the cursor to that cell and press .

Setting Up the Table from the Home Screen or a Program

To store a value to TblStart, @Tbl, or TblZnput from the home screen or a program, select the variable name from the VARS TABLE secondary menu. TblZnput is a list of independent-variable values in the current table.

When you press y - in the program editor, you can select IndpntAuto, IndpntAsk, DependAuto, and DependAsk.

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Defining the Dependent Variables

Defining Dependent Variables from the Y= Editor

In the Y= editor, enter the functions that define the dependent variables. Only functions that are selected in the Y= editor are displayed in the table. The current graphing mode is used. In Par mode, you must define both components of each parametric equation (Chapter 4).

Editing Dependent Variables from the Table Editor

To edit a selected Y= function from the table editor, follow these steps.

1. Press y 0 to display the table, then press ~ or | to move the cursor to a dependent-variable column.

2. Press } until the cursor is on the function name at the top of the column. The function is displayed on the bottom line.

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3. Press . The cursor moves to the bottom line. Edit the function.

4. Press or . The new values are calculated. The table and the Y= function are updated automatically.

Note: You also can use this feature to view the function that defines a dependent variable without having to leave the table.

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Displaying the Table

The Table

To display the table, press y 0.

Current cell

Independent-variable values in the first column

Dependent-variable values in the second and third columns

Current cells full value

Note: The table abbreviates the values, if necessary.

Independent and Dependent Variables

The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1). In the table above, for example, the independent variable X and the dependent variables Y1 and Y2 are displayed because Func graphing mode is set.

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Graphing Mode Independent Variable Dependent Variable

Func (function) X Y1 through Y9, and Y0

Par (parametric) T X1T/Y1T through X6T/Y6T

Pol (polar) q r1 through r6

Seq (sequence) n u(n), v(n), and w(n)

Clearing the Table from the Home Screen or a Program

From the home screen, select the ClrTable instruction from the CATALOG. To clear the table, press .

From a program, select 9:ClrTable from the PRGM I/O menu or from the CATALOG. The table is cleared upon execution. If IndpntAsk is selected, all independent and dependent variable values on the table are cleared. If DependAsk is selected, all dependent variable values on the table are cleared.

Scrolling Independent-Variable Values

If Indpnt: Auto is selected, you can press } and in the independent- variable column to display more values. As you scroll the column, the corresponding dependent-variable values also are displayed. All dependent-variable values may not be displayed if Depend: Ask is selected.

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Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table. In the example above, TblStart=0 and @Tbl=1 generates and displays values of X=0, , 6; but you can press } to scroll back and display the table for X=M1, , 5.

Displaying Other Dependent Variables

If you have defined more than two dependent variables, the first two selected Y= functions are displayed initially. Press ~ or | to display dependent variables defined by other selected Y= functions. The independent variable always remains in the left column, except during a trace with Par graphing mode and G.T split-screen mode set.

Tip: To simultaneously display two dependent variables on the table that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display. For example, to simultaneously display Y4 and Y7 on the table, go to the Y= editor and deselect Y5 and Y6.

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Chapter 8: Draw Instructions

Getting Started: Drawing a Tangent Line

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to find the equation of the tangent line at X = 2/2 for the function Y = sin(X).

Before you begin, select Radian and Func mode from the mode screen, if necessary.

1. Press o to display the Y= editor. Press to store sin(X) in Y1.

2. Press q 7 to select 7:ZTrig, which graphs the equation in the Zoom Trig window.

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3. Press y < 5 to select 5:Tangent(. The tangent instruction is initiated.

4. Press y C 2 2.

5. Press . The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph.

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Using the DRAW Menu

DRAW Menu

To display the DRAW menu, press y <. The TI-83 Pluss interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph.

DRAW POINTS STO

1:ClrDraw Clears all drawn elements. 2:Line( Draws a line segment between 2 points. 3:Horizontal Draws a horizontal line. 4:Vertical Draws a vertical line. 5:Tangent( Draws a line segment tangent to a function. 6:DrawF Draws a function. 7:Shade( Shades an area between two functions. 8:DrawInv Draws the inverse of a function. 9:Circle( Draws a circle. 0:Text( Draws text on a graph screen. A:Pen Activates the free-form drawing tool.

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Before Drawing on a Graph

The DRAW instructions draw on top of graphs. Therefore, before you use the DRAW instructions, consider whether you want to perform one or more of the following actions.

Change the mode settings on the mode screen.

Change the format settings on the format screen.

Enter or edit functions in the Y= editor.

Select or deselect functions in the Y= editor.

Change the window variable values.

Turn stat plots on or off.

Clear existing drawings with ClrDraw.

Note: If you draw on a graph and then perform any of the actions listed above, the graph is replotted without the drawings when you display the graph again.

Drawing on a Graph

You can use any DRAW menu instructions except DrawInv to draw on Func, Par, Pol, and Seq graphs. DrawInv is valid only in Func graphing. The coordinates for all DRAW instructions are the displays x-coordinate and y-coordinate values.

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You can use most DRAW menu and DRAW POINTS menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a DRAW

menu instruction, the home screen is displayed.

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Clearing Drawings

Clearing Drawings When a Graph Is Displayed

All points, lines, and shading drawn on a graph with DRAW instructions are temporary.

To clear drawings from the currently displayed graph, select 1:ClrDraw from the DRAW menu. The current graph is replotted and displayed with no drawn elements.

Clearing Drawings from the Home Screen or a Program

To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor. Select 1:ClrDraw from the DRAW menu. The instruction is copied to the cursor location. Press .

When ClrDraw is executed, it clears all drawings from the current graph and displays the message Done. When you display the graph again, all drawn points, lines, circles, and shaded areas will be gone.

Note: Before you clear drawings, you can store them with StorePic.

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Drawing Line Segments

Drawing a Line Segment Directly on a Graph

To draw a line segment when a graph is displayed, follow these steps.

1. Select 2:Line( from the DRAW menu.

2. Place the cursor on the point where you want the line segment to begin, and then press .

3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press .

To continue drawing line segments, repeat steps 2 and 3. To cancel Line(, press .

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Drawing a Line Segment from the Home Screen or a Program

Line( also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values may be entered as expressions.

Line(X1,Y1,X2,Y2)

To erase a line segment, enter Line(X1,Y1,X2,Y2,0)

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Drawing Horizontal and Vertical Lines

Drawing a Line Directly on a Graph

To draw a horizontal or vertical line when a graph is displayed, follow these steps.

1. Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is displayed that moves as you move the cursor.

2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass.

3. Press to draw the line on the graph.

To continue drawing lines, repeat steps 2 and 3.

To cancel Horizontal or Vertical, press .

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Drawing a Line from the Home Screen or a Program

Horizontal (horizontal line) draws a horizontal line at Y=y. y can be an expression but not a list.

Horizontal y

Vertical (vertical line) draws a vertical line at X=x. x can be an expression but not a list.

Vertical x

To instruct the TI-83 Plus to draw more than one horizontal or vertical line, separate each instruction with a colon ( : ).

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Drawing Tangent Lines

Drawing a Tangent Line Directly on a Graph

To draw a tangent line when a graph is displayed, follow these steps.

1. Select 5:Tangent( from the DRAW menu.

2. Press and } to move the cursor to the function for which you want to draw the tangent line. The current graphs Y= function is displayed in the top-left corner, if ExprOn is selected.

3. Press ~ and | or enter a number to select the point on the function at which you want to draw the tangent line.

4. Press . In Func mode, the X value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the dy/dx value is displayed.

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Tip: Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for X and the equation for Y.

Drawing a Tangent Line from the Home Screen or a Program

Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X2, at point X=value. X can be an expression. expression is interpreted as being in Func mode.

Tangent(expression,value)

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Drawing Functions and Inverses

Drawing a Function

DrawF (draw function) draws expression as a function in terms of X on the current graph. When you select 6:DrawF from the DRAW menu, the TI-83 Plus returns to the home screen or the program editor. DrawF is not interactive.

DrawF expression

Note: You cannot use a list in expression to draw a family of curves.

Drawing an Inverse of a Function

DrawInv (draw inverse) draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis. When you select 8:DrawInv from the DRAW menu, the TI-83 Plus returns to the home screen or the program editor. DrawInv is not interactive. DrawInv works in Func mode only.

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DrawInv expression

Note: You cannot use a list in expression to draw a family of curves.

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Shading Areas on a Graph

Shading a Graph

To shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is pasted to the home screen or to the program editor.

Shade( draws lowerfunc and upperfunc in terms of X on the current graph and shades the area that is specifically above lowerfunc and below upperfunc. Only the areas where lowerfunc < upperfunc are shaded.

Xleft and Xright, if included, specify left and right boundaries for the shading. Xleft and Xright must be numbers between Xmin and Xmax, which are the defaults.

pattern specifies one of four shading patterns.

pattern=1 vertical (default) pattern=2 horizontal pattern=3 negativeslope 45 pattern=4 positiveslope 45

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patres specifies one of eight shading resolutions.

patres=1 shades every pixel (default) patres=2 shades every second pixel patres=3 shades every third pixel patres=4 shades every fourth pixel patres=5 shades every fifth pixel patres=6 shades every sixth pixel patres=7 shades every seventh pixel patres=8 shades every eighth pixel

Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres])

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Drawing Circles

Drawing a Circle Directly on a Graph

To draw a circle directly on a displayed graph using the cursor, follow these steps.

1. Select 9:Circle( from the DRAW menu.

2. Place the cursor at the center of the circle you want to draw. Press .

3. Move the cursor to a point on the circumference. Press to draw the circle on the graph.

Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display. When you use the Circle( instruction from the home screen or a program, the current window variables may distort the shape.

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To continue drawing circles, repeat steps 2 and 3. To cancel Circle(, press .

Drawing a Circle from the Home Screen or a Program

Circle( draws a circle with center (X,Y) and radius. These values can be expressions.

Circle(X,Y,radius)

Tip: When you use Circle( on the home screen or from a program, the current window values may distort the drawn circle. Use ZSquare (Chapter 3) before drawing the circle to adjust the window variables and make the circle circular.

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Placing Text on a Graph

Placing Text Directly on a Graph

To place text on a graph when the graph is displayed, follow these steps.

1. Select 0:Text( from the DRAW menu.

2. Place the cursor where you want the text to begin.

3. Enter the characters. Press or y 7 to enter letters and q. You may enter TI-83 Plus functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.

To cancel Text(, press .

Placing Text on a Graph from the Home Screen or a Program

Text( places on the current graph the characters comprising value, which can include TI-83 Plus functions and instructions. The top-left corner of the first character is at pixel (row,column), where row is an integer between 0 and 57 and column is an integer between 0 and 94. Both row and column can be expressions.

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Text(row,column,value,value)

value can be text enclosed in quotation marks ( " ), or it can be an expression. The TI-83 Plus will evaluate an expression and display the result with up to 10 characters.

Split Screen

On a Horiz split screen, the maximum value for row is 25. On a G.T split screen, the maximum value for row is 45, and the maximum value for column is 46.

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Using Pen to Draw on a Graph

Using Pen to Draw on a Graph

Pen draws directly on a graph only. You cannot execute Pen from the home screen or a program.

To draw on a displayed graph, follow these steps.

1. Select A:Pen from the DRAW menu.

2. Place the cursor on the point where you want to begin drawing. Press to turn on the pen.

3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time.

4. Press to turn off the pen.

For example, Pen was used to create the arrow pointing to the local minimum of the selected function.

Note: To continue drawing on the graph, move the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel Pen, press .

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Drawing Points on a Graph

DRAW POINTS Menu

To display the DRAW POINTS menu, press y < ~. The TI-83 Pluss interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph.

DRAW POINTS STO 1:Pt-On( Turns on a point. 2:Pt-Off( Turns off a point. 3:Pt-Change( Toggles a point on or off. 4:Pxl-On( Turns on a pixel. 5:Pxl-Off( Turns off a pixel. 6:Pxl-Change( Toggles a pixel on or off. 7:pxl-Test( Returns 1 if pixel on, 0 if pixel off.

Drawing Points Directly on a Graph with Pt.On(

To draw a point on a graph, follow these steps.

1. Select 1:Pt.On( from the DRAW POINTS menu.

2. Move the cursor to the position where you want to draw the point.

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3. Press to draw the point.

To continue drawing points, repeat steps 2 and 3. To cancel Pt.On(, press .

Erasing Points with Pt.Off(

To erase (turn off) a drawn point on a graph, follow these steps.

1. Select 2:Pt.Off( (point off) from the DRAW POINTS menu.

2. Move the cursor to the point you want to erase.

3. Press to erase the point.

To continue erasing points, repeat steps 2 and 3. To cancel Pt.Off(, press .

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Changing Points with Pt.Change(

To change (toggle on or off) a point on a graph, follow these steps.

1. Select 3:Pt.Change( (point change) from the DRAW POINTS menu.

2. Move the cursor to the point you want to change.

3. Press to change the points on/off status.

To continue changing points, repeat steps 2 and 3. To cancel Pt.Change(, press .

Drawing Points from the Home Screen or a Program

Pt.On( (point on) turns on the point at (X=x,Y=y). Pt.Off( turns the point off. Pt.Change( toggles the point on or off. mark is optional; it determines the points appearance; specify 1, 2, or 3, where:

1 = (dot; default) 2 = (box) 3 = + (cross)

Pt.On(x,y[,mark]) Pt.Off(x,y[,mark]) Pt.Change(x,y)

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Note: If you specified mark to turn on a point with Pt.On(, you must specify mark when you turn off the point with Pt.Off(. Pt.Change( does not have the mark option.

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Drawing Pixels

TI-83 Plus Pixels

A pixel is a square dot on the TI-83 Plus display. The Pxl. (pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from the DRAW

POINTS menu, the TI-83 Plus returns to the home screen or the program editor. The pixel instructions are not interactive.

Turning On and Off Pixels with Pxl.On( and Pxl.Off(

Pxl.On( (pixel on) turns on the pixel at (row,column), where row is an integer between 0 and 62 and column is an integer between 0 and 94.

Pxl.Off( turns the pixel off. Pxl.Change( toggles the pixel on and off.

Pxl.On(row,column) Pxl.Off(row,column) Pxl.Change(row,column)

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Using pxl.Test(

pxl.Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off on the current graph. row must be an integer between 0 and 62. column must be an integer between 0 and 94.

pxl.Test(row,column)

Split Screen

On a Horiz split screen, the maximum value for row is 30 for Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(.

On a G.T split screen, the maximum value for row is 50 and the maximum value for column is 46 for Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(.

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Storing Graph Pictures (Pic)

DRAW STO Menu

To display the DRAW STO menu, press y < |. When you select an instruction from the DRAW STO menu, the TI-83 Plus returns to the home screen or the program editor. The picture and graph database instructions are not interactive.

DRAW POINTS STO

1: StorePic Stores the current picture. 2: RecallPic Recalls a saved picture. 3: StoreGDB Stores the current graph database. 4: RecallGDB Recalls a saved graph database.

Storing a Graph Picture

You can store up to 10 graph pictures, each of which is an image of the current graph display, in picture variables Pic1 through Pic9, or Pic0. Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program.

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A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display hidden by these items are stored with the picture.

To store a graph picture, follow these steps.

1. Select 1:StorePic from the DRAW STO menu. StorePic is pasted to the current cursor location.

2. Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store the picture. For example, if you enter 3, the TI-83 Plus will store the picture to Pic3.

Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to StorePic.

3. Press to display the current graph and store the picture.

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Recalling Graph Pictures (Pic)

Recalling a Graph Picture

To recall a graph picture, follow these steps.

1. Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the current cursor location.

2. Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture. For example, if you enter 3, the TI-83 Plus will recall the picture stored to Pic3.

Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to RecallPic.

3. Press to display the current graph with the picture superimposed on it.

Note: Pictures are drawings. You cannot trace a curve that is part of a picture.

Deleting a Graph Picture

To delete graph pictures from memory, use the MEMORY MANAGEMENT /DELETE secondary menu(Chapter 18).

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Storing Graph Databases (GDB)

What Is a Graph Database?

A graph database (GDB) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10 GDBs in variables GDB1 through GDB9, or GDB0 and recall them to recreate graphs.

A GDB stores five elements of a graph.

Graphing mode Window variables Format settings All functions in the Y= editor and the selection status of each Graph style for each Y= function

GDBs do not contain drawn items or stat plot definitions.

Storing a Graph Database

To store a graph database, follow these steps.

1. Select 3:StoreGDB from the DRAW STO menu. StoreGDB is pasted to the current cursor location.

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2. Enter the number (from 1 to 9, or 0) of the GDB variable to which you want to store the graph database. For example, if you enter 7, the TI-83 Plus will store the GDB to GDB7.

Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted next to StoreGDB.

3. Press to store the current database to the specified GDB

variable.

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Recalling Graph Databases (GDB)

Recalling a Graph Database

CAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing the current Y= functions to another database before recalling a stored GDB.

To recall a graph database, follow these steps.

1. Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to the current cursor location.

2. Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to recall a GDB. For example, if you enter 7, the TI-83 Plus will recall the GDB stored to GDB7.

Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted next to RecallGDB.

3. Press to replace the current GDB with the recalled GDB. The new graph is not plotted. The TI-83 Plus changes the graphing mode automatically, if necessary.

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Deleting a Graph Database

To delete a GDB from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18).

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Chapter 9: Split Screen

Getting Started: Exploring the Unit Circle

Getting Started is a fast-paced introduction. Read the chapter for details.

Use G.T (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0, 30, 45, 60, 90, and so on.

1. Press z to display the mode screen. Press ~ to select Degree mode. Press ~ to select Par (parametric) graphing mode.

Press ~ ~ to select G.T (graph-table) split-screen mode.

2. Press y. to display the format screen. Press ~ to select ExprOff.

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3. Press o to display the Y= editor for Par graphing mode. Press to store cos(T) to X1T. Press to store sin(T) to Y1T.

4. Press p to display the window editor. Enter these values for the window variables.

Tmin=0 Xmin=L2.3 Ymin=L2.5 Tmax=360 Xmax=2.3 Ymax=2.5 Tstep=15 Xscl=1 Yscl=1

5. Press r. On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated. When T=0 (from the graph trace coordinates), you can see from the table on the right that the value of X1T (cos(T)) is 1 and Y1T (sin(T)) is 0. Press ~ to move the cursor to the next 15 angle increment. As you trace around the circle in steps of 15, an approximation of the standard value for each angle is highlighted in the table.

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Using Split Screen

Setting a Split-Screen Mode

To set a split-screen mode, press z, and then move the cursor to the bottom line of the mode screen.

Select Horiz (horizontal) to display the graph screen and another screen split horizontally.

Select G.T (graph-table) to display the graph screen and table screen split vertically.

$ $

The split screen is activated when you press any key that applies to either half of the split screen.

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Some screens are never displayed as split screens. For example, if you press z in Horiz or G.T mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns.

When you press a key or key combination in either Horiz or G.T mode, the cursor is placed in the half of the display for which that key applies. For example, if you press r, the cursor is placed in the half in which the graph is displayed. If you press y 0, the cursor is placed in the half in which the table is displayed.

The TI-83 Plus will remain in split-screen mode until you change back to Full screen mode.

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Horiz (Horizontal) Split Screen

Horiz Mode

In Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves.

The top half displays the graph.

The bottom half displays any of these editors.

Home screen (four lines)

Y= editor (four lines)

Stat list editor (two rows)

Window editor (three settings)

Table editor (two rows)

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Moving from Half to Half in Horiz Mode

To use the top half of the split screen:

Press or .

Select a ZOOM or CALC operation.

To use the bottom half of the split screen:

Press any key or key combination that displays the home screen.

Press o (Y= editor).

Press (stat list editor).

Press p (window editor).

Press y 0 (table editor).

Full Screens in Horiz Mode

All other screens are displayed as full screens in Horiz split-screen mode.

To return to the Horiz split screen from a full screen when in Horiz mode, press any key or key combination that displays the graph, home screen, Y= editor, stat list editor, window editor, or table editor.

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G.T (Graph-Table) Split Screen

G.T Mode

In G.T (graph-table) split-screen mode, a vertical line splits the screen into left and right halves.

The left half displays the graph.

The right half displays the table.

Moving from Half to Half in G.T Mode

To use the left half of the split screen:

Press or .

Select a ZOOM or CALC operation.

To use the right half of the split screen, press y 0.

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Using r in G.T Mode

As you move the trace cursor along a graph in the split screens left half in G.T mode, the table on the right half automatically scrolls to match the current cursor values.

Note: When you trace in Par graphing mode, both components of an equation (XnT and YnT) are displayed in the two columns of the table. As you trace, the current value of the independent variable T is displayed on the graph.

Full Screens in G.T Mode

All screens other than the graph and the table are displayed as full screens in G.T split-screen mode.

To return to the G.T split screen from a full screen when in G.T mode, press any key or key combination that displays the graph or the table.

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TI-83 Plus Pixels in Horiz and G.T Modes

TI-83 Plus Pixels in Horiz and G.T Modes

Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on.

DRAW POINTS Menu Pixel Instructions

For Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(:

In Horiz mode, row must be {30; column must be {94.

In G.T mode, row must be {50; column must be {46.

Pxl.On(row,column)

DRAW Menu Text( Instruction

For the Text( instruction:

In Horiz mode, row must be {25; column must be {94.

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In G.T mode, row must be {45; column must be {46.

Text(row,column,"text")

PRGM I/O Menu Output( Instruction

For the Output( instruction:

In Horiz mode, row must be {4; column must be {16.

In G.T mode, row must be {8; column must be {16.

Output(row,column,"text")

Setting a Split-Screen Mode from the Home Screen or a Program

To set Horiz or G.T from a program, follow these steps.

1. Press z while the cursor is on a blank line in the program editor.

2. Select Horiz or G.T.

The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution.

Note: You also can paste Horiz or G.T to the home screen or program editor from the CATALOG (Chapter 15).

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Chapter 10: Matrices

Getting Started: Systems of Linear Equations

Getting Started is a fast-paced introduction. Read the chapter for details.

Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83 Plus, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form.

1. Press y >. Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A]

2. Press 2 4 to define a 24 matrix. The rectangular cursor indicates the current element. Ellipses (...) indicate additional columns beyond the screen.

3. Press 1 to enter the first element. The rectangular cursor moves to the second column of the first row.

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4. Press 2 3 3 to complete the first row for X + 2Y + 3Z = 3.

5. Press 2 3 4 3 to enter the second row for 2X + 3Y + 4Z = 3.

6. Press y 5 to return to the home screen. If necessary, press to clear the home screen. Press y > ~ to display the MATRX MATH menu. Press } to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen.

7. Press y > 1 to select 1: [A] from the MATRX NAMES menu. Press . The reduced row-echelon form of the matrix is displayed and stored in Ans.

1X N 1Z = L3 therefore X = L3 + Z 1Y + 2Z = 3 therefore Y = 3 N 2Z

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Defining a Matrix

What Is a Matrix?

A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. The TI-83 Plus has 10 matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-83 Plus matrices.

Selecting a Matrix

Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps.

1. Press y > | to display the MATRX EDIT menu. The dimensions of any previously defined matrices are displayed.

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2. Select the matrix you want to define. The MATRX EDIT screen is displayed.

Accepting or Changing Matrix Dimensions

The dimensions of the matrix (row column) are displayed on the top line. The dimensions of a new matrix are 1 1. You must accept or change the dimensions each time you edit a matrix. When you select a matrix to define, the cursor highlights the row dimension.

To accept the row dimension, press .

To change the row dimension, enter the number of rows (up to 99), and then press .

The cursor moves to the column dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press , the rectangular cursor moves to the first matrix element.

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Viewing and Editing Matrix Elements

Displaying Matrix Elements

After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero.

Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary. The full value of the current element, which is indicated by the rectangular cursor, is displayed on the bottom line.

This is an 8 4 matrix. Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate additional rows.

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Deleting a Matrix

To delete matrices from memory, use the MEMORY MANAGEMENT/DELETE

secondary menu (Chapter 18).

Viewing a Matrix

The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line.

Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.

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Viewing-Context Keys

Key Function

| or ~ Moves the rectangular cursor within the current row

or } Moves the rectangular cursor within the current column; on the top row, } moves the cursor to the column dimension; on the column dimension, } moves the cursor to the row dimension

Switches to editing context; activates the edit cursor on the bottom line

Switches to editing context; clears the value on the bottom line

Any entry character Switches to editing context; clears the value on the bottom line; copies the character to the bottom line

y 6 Nothing

{ Nothing

Editing a Matrix Element

In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps.

1. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.

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2. Press |, }, ~, and to move the cursor to the matrix element you want to change.

3. Switch to editing context by pressing , , or an entry key.

4. Change the value of the matrix element using the editing-context keys described below. You may enter an expression, which is evaluated when you leave editing context.

Note: You can press to restore the value at the rectangular cursor if you make a mistake.

5. Press , }, or to move to another element.

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Editing-Context Keys

Key Function

| or ~ Moves the edit cursor within the value

or } Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor within the column

Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor to the next row element

Clears the value on the bottom line

Any entry character Copies the character to the location of the edit cursor on the bottom line

y 6 Activates the insert cursor

{ Deletes the character under the edit cursor on the bottom line

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Using Matrices with Expressions

Using a Matrix in an Expression

To use a matrix in an expression, you can do any of the following.

Copy the name from the MATRX NAMES menu.

Recall the contents of the matrix into the expression with y K (Chapter 1).

Enter the matrix directly (see below).

Entering a Matrix in an Expression

You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression.

To enter a matrix in an expression, follow these steps.

1. Press y [ [ ] to indicate the beginning of the matrix.

2. Press y [ [ ] to indicate the beginning of a row.

3. Enter a value, which can be an expression, for each element in the row. Separate the values with commas.

4. Press y [ ] ] to indicate the end of a row.

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5. Repeat steps 2 through 4 to enter all of the rows.

6. Press y [ ] ] to indicate the end of the matrix.

Note: The closing ]] are not necessary at the end of an expression or preceding !.

The resulting matrix is displayed in the form:

[[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]]

Any expressions are evaluated when the entry is executed.

Note: The commas that you must enter to separate elements are not displayed on output.

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Displaying and Copying Matrices

Displaying a Matrix

To display the contents of a matrix on the home screen, select the matrix from the MATRX NAMES menu, and then press .

Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate additional rows. Press ~, |, , and } to scroll the matrix.

Copying One Matrix to Another

To copy a matrix, follow these steps.

1. Press y > to display the MATRX NAMES menu.

2. Select the name of the matrix you want to copy.

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3. Press .

4. Press y > again and select the name of the new matrix to which you want to copy the existing matrix.

5. Press to copy the matrix to the new matrix name.

Accessing a Matrix Element

On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select matrix from the MATRX NAMES

menu.

[matrix](row,column)

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Using Math Functions with Matrices

Using Math Functions with Matrices

You can use many of the math functions on the TI-83 Plus keyboard, the MATH menu, the MATH NUM menu, and the MATH TEST menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same.

+ (Add), (Subtract), (Multiply)

To add () or subtract () matrices, the dimensions must be the same. The answer is a matrix in which the elements are the sum or difference of the individual corresponding elements.

matrixA+matrixB matrixANmatrixB

To multiply () two matrices together, the column dimension of matrixA must match the row dimension of matrixB.

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matrixAmatrixB

Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value.

matrixvalue valuematrix

L (Negation)

Negating a matrix () returns a matrix in which the sign of every element is changed (reversed).

Lmatrix

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abs(

abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of each element of matrix.

abs(matrix)

round(

round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits.

round(matrix[,#decimals])

M1 (Inverse)

Use the L1 function () to invert a matrix (^L1 is not valid). matrix must be square. The determinant cannot equal zero.

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matrixL1

Powers

To raise a matrix to a power, matrix must be square. You can use 2 (), 3 (MATH menu), or ^power () for integer power between 0 and 255.

matrix2

matrix3

matrix^power

Relational Operations

To compare two matrices using the relational operations = and (TEST

menu), they must have the same dimensions. = and compare matrixA and matrixB on an element-by-element basis. The other relational operations are not valid with matrices.

matrixA=matrixB returns 1 if every comparison is true; it returns 0 if any comparison is false.

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matrixAmatrixB returns 1 if at least one comparison is false; it returns 0 if no comparison is false.

iPart(, fPart(, int(

iPart( (integer part), fPart( (fractional part), and int( (greatest integer) are on the MATH NUM menu.

iPart( returns a matrix containing the integer part of each element of matrix.

fPart( returns a matrix containing the fractional part of each element of matrix.

int( returns a matrix containing the greatest integer of each element of matrix.

iPart(matrix) fPart(matrix) int(matrix)

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Using the MATRX MATH Operations

MATRX MATH Menu

To display the MATRX MATH menu, press y > ~.

NAMES MATH EDIT 1: det( Calculates the determinant. 2: T Transposes the matrix. 3: dim( Returns the matrix dimensions. 4: Fill( Fills all elements with a constant. 5: identity( Returns the identity matrix. 6: randM( Returns a random matrix. 7: augment( Appends two matrices. 8: Matr4list( Stores a matrix to a list. 9: List4matr( Stores a list to a matrix. 0: c*msum( Returns the cumulative sums of a matrix. A: ref( Returns the row-echelon form of a matrix. B: rref( Returns the reduced row-echelon form. C: rowSwap( Swaps two rows of a matrix. D: row+( Adds two rows; stores in the second row. E: row( Multiplies the row by a number. F: row+( Multiplies the row, adds to the second row.

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det(

det( (determinant) returns the determinant (a real number) of a square matrix.

det(matrix)

T (Transpose)

T (transpose) returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of matrix.

matrixT

Accessing Matrix Dimensions with dim(

dim( (dimension) returns a list containing the dimensions ({rowscolumns}) of matrix.

dim(matrix)

Note: dim(matrix)!Ln:Ln(1) returns the number of rows. dim(matrix)!Ln:Ln(2) returns the number of columns.

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Creating a Matrix with dim(

Use dim( with to create a new matrixname of dimensions rows columns with 0 as each element.

{rows,columns}!dim(matrixname)

Redimensioning a Matrix with dim(

Use dim( with to redimension an existing matrixname to dimensions rows columns. The elements in the old matrixname that are within the new dimensions are not changed. Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted.

{rows,columns}!dim(matrixname)

Fill(

Fill( stores value to every element in matrixname.

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Fill(value,matrixname)

identity(

identity( returns the identity matrix of dimension rows dimension columns.

identity(dimension)

randM(

randM( (create random matrix) returns a rows columns random matrix of integers L9 and 9. The seed value stored to the rand function controls the values (Chapter 2).

randM(rows,columns)

augment(

augment( appends matrixA to matrixB as new columns. matrixA and matrixB both must have the same number of rows.

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augment(matrixA,matrixB)

Matr4list(

Matr4list( (matrix stored to list) fills each listname with elements from each column in matrix. Matr4list( ignores extra listname arguments. Likewise, Matr4list( ignores extra matrix columns.

Matr4list(matrix,listnameA,...,listname n)

&

Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with a specific column from matrix, you must enter column# after matrix.

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Matr4list(matrix,column#,listname)

&

List4matr(

List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If dimensions of all lists are not equal, List4matr( fills each extra matrixname row with 0. Complex lists are not valid.

List4matr(listA,...,list n,matrixname)

&

c*msum(

c*msum( returns cumulative sums of the elements in matrix, starting with the first element. Each element is the cumulative sum of the column from top to bottom.

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c*msum(matrix)

Row Operations

MATRX MATH menu items A through F are row operations. You can use a row operation in an expression. Row operations do not change matrix in memory. You can enter all row numbers and values as expressions. You can select the matrix from the MATRX NAMES menu.

ref(, rref(

ref( (row-echelon form) returns the row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows.

ref(matrix)

rref( (reduced row-echelon form) returns the reduced row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows.

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rref(matrix)

rowSwap(

rowSwap( returns a matrix. It swaps rowA and rowB of matrix.

rowSwap(matrix,rowA,rowB)

row+(

row+( (row addition) returns a matrix. It adds rowA and rowB of matrix and stores the results in rowB.

row+(matrix,rowA,rowB)

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row(

row( (row multiplication) returns a matrix. It multiplies row of matrix by value and stores the results in row.

row(value,matrix,row)

row+(

row+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by value, adds it to rowB, and stores the results in rowB.

row+(value,matrix,rowA,rowB)

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Chapter 11: Lists

Getting Started: Generating a Sequence

Getting Started is a fast-paced introduction. Read the chapter for details.

Calculate the first eight terms of the sequence 1/A2. Store the results to a user- created list. Then display the results in fraction form. Begin this example on a blank line on the home screen.

1. Press y 9 ~ to display the LIST OPS menu.

2. Press 5 to select 5:seq(, which pastes seq( to the current cursor location.

3. Press 1 [A] [A] 1 8 1 to enter the sequence.

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4. Press , and then press y to turn on alpha-lock. Press [S] [E] [Q], and then press to turn off alpha-lock. Press 1 to complete the list name.

5. Press to generate the list and store it in SEQ1. The list is displayed on the home screen. An ellipsis (...) indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

6. Press y 9 to display the LIST NAMES menu. Press 7 to select 7:seq( to paste SEQ1 to the current cursor location. (If SEQ1 is not item 7 on your LIST NAMES menu, move the cursor to SEQ1 before you press .)

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7. Press to display the MATH menu. Press 1 to select 1:4Frac, which pastes 4Frac to the current cursor location.

8. Press to show the sequence in fraction form. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

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Naming Lists

Using TI-83 Plus List Names L1 through L6

The TI-83 Plus has six list names in memory: L1, L2, L3, L4, L5, and L6. The list names L1 through L6 are on the keyboard above the numeric keys through . To paste one of these names to a valid screen, press y, and then press the appropriate key. L1 through L6 are stored in stat list editor columns 1 through 6 when you reset memory.

Creating a List Name on the Home Screen

To create a list name on the home screen, follow these steps.

1. Press y E, enter one or more list elements, and then press y F. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions.

2. Press .

3. Press [letter from A to Z or q] to enter the first letter of the name.

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4. Enter zero to four letters, q, or numbers to complete the name.

5. Press . The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the LIST NAMES menu.

Note: If you want to view a user-created list in the stat list editor, you must store it in the stat list editor (Chapter 12).

You also can create a list name in these four places.

At the Name= prompt in the stat list editor

At an Xlist:, Ylist:, or Data List: prompt in the stat plot editor

At a List:, List1:, List2:, Freq:, Freq1:, Freq2:, XList:, or YList: prompt in the inferential stat editors

On the home screen using SetUpEditor

You can create as many list names as your TI-83 Plus memory has space to store.

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Storing and Displaying Lists

Storing Elements to a List

You can store list elements in either of two ways.

Use braces and on the home screen.

Use the stat list editor (Chapter 12).

The maximum dimension of a list is 999 elements.

Tip: When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter real(listname)!listname.

Displaying a List on the Home Screen

To display the elements of a list on the home screen, enter the name of the list (preceded by , if necessary, and then press . An ellipsis indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.

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Copying One List to Another

To copy a list, store it to another list.

Accessing a List Element

You can store a value to or recall a value from a specific list element. You can store to any element within the current list dimension or one element beyond.

listname(element)

Deleting a List from Memory

To delete lists from memory, including L1 through L6, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Resetting memory restores L1 through L6. Removing a list from the stat list editor does not delete it from memory.

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Using Lists in Graphing

You can use lists to graph a family of curves (Chapter 3).

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Entering List Names

Using the LIST NAMES Menu

To display the LIST NAMES menu, press y 9. Each item is a user- created list name. LIST NAMES menu items are sorted automatically in alphanumerical order. Only the first 10 items are labeled, using 1 through 9, then 0. To jump to the first list name that begins with a particular alpha character or q, press [letter from A to Z or q].

Tip: From the top of a menu, press } to move to the bottom. From the bottom, press to move to the top.

Note: The LIST NAMES menu omits list names L1 through L6. Enter L1 through L6 directly from the keyboard.

When you select a list name from the LIST NAMES menu, the list name is pasted to the current cursor location.

The list name symbol precedes a list name when the name is pasted where non-list name data also is valid, such as the home screen.

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The symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editors Name= prompt or the stat plot editors XList: and YList: prompts.

Entering a User-Created List Name Directly