GRAPHING CALCULATOR KEYSTROKE GUIDE

GRAPHING CALCULATOR KEYSTROKE GUIDE to accompany ELEMENTARY ALGEBRA: DISCOVERY AND VISUALIZATION 2nd Edition Karl M. Zilm Lewis & Clark Community College HOUGHTON MIFFLIN COMPANY BOSTON NEW YORK

Editor in Chief: Charles Hartford Associate Editor: Mary Beckwith Senior Manufacturing Coordinator: Sally Culler Marketing Manager: Ros Kane Copyright 1999 by Houghton Mifflin Company. All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system without prior written permission of Houghton Mifflin Company unless such copying is expressly permitted by federal copyright law. Address inquiries to College Permissions, Houghton Mifflin Company, 222 Berkeley Street, Boston, MA 02116-3764. Printed in the U.S.A. ISBN: 0-395-937736 123456789-HS-03 02 01 00 99

Preface This Guide is designed for students using a Texas Instruments TI-82 or TI-83 graphing calculator in conjunction with the textbook Elementary Algebra: Discovery and Visualization, 2nd edition, by Hubbard and Robinson. There is a separate section of the Guide for each calculator model. The TI-82 section begins on page 1; the TI-83 section begins on page 27. The following description of the Guide and how to use it applies to both sections. The Guide assumes no prior experience in using a graphing calculator. Therefore, it begins with an Introduction chapter dealing with the basics: how to turn the calculator on, how to turn it off, how to adjust the screen contrast, and how to enter and edit basic arithmetic expressions. You should probably go through the Introduction chapter of this Guide as soon as you get your calculator. The Introduction chapter will give you an opportunity to familiarize yourself with the basic operation of your calculator so that you will be ready to learn the other features described later in the Guide. The Introduction chapter is followed by the Graphing Calculator Keystroke Guide, which is keyed to the textbook. As you look at the pages in the textbook, you will notice that in the left margin of some pages a book icon appears next to a key word or phrase, with a brief reference to a related feature on the graphing calculator appearing in the body of the text. Corresponding to each of these key words or phrases in the textbook, this Guide provides a detailed description of how to use the related feature on your particular graphing calculator model. In the Guide each key word or phrase is printed as it appears in the textbook, and on the line above it is the number of the page on which it appears in the textbook. Each key word or phrase will also have its own number (in boldface type) for easy future reference. For example, on page 14 in the textbook you will find a book icon in the left margin with the key words Absolute Value next to it and a brief reference in the body of the text to the calculator notation ABS. If you are using a TI-82 graphing calculator, look on page 9 in this Guide. If you are using a TI-83, look on page 35 in this Guide. You will see a reference to the absolute value feature: page 14 10 Absolute Value, followed by a description of how to enter expressions involving absolute values on your calculator. The boldface number 10 is a reference number which may be used later in the Guide to refer you quickly to this description of the absolute value feature. As you begin to use the Guide to read about the key words and phrases, you may want to keep a bookmark in the Guide at the most recently examined key word or phrase. If you go through the chapters of the textbook in the order they are printed, you will encounter the new key words and phrases in the order they are printed in this Guide. Thus, your bookmark will usually be at or near the next key word or phrase you will want to read about, and you will be able to refer to it quickly when needed. I would like to thank the authors of the textbook, Elaine Hubbard and Ronald D. Robinson, and the staff of Houghton Mifflin, particularly Charles Hartford, Editor in Chief; and Kathy Yoon, Editorial Assistant, for their support and assistance in the production of this Guide. Karl M. Zilm iii

Contents TI-82 INTRODUCTION: On/Off, Contrast, Mode, and Editing Expressions 1 Turning the Calculator On 1 Adjusting the Display Contrast (Making the Screen Lighter or Darker) 1 Turning the Calculator Off 2 Second Functions for Keys Notation 2 Mode 2 Editing Expressions 3 TI-82 GRAPHING CALCULATOR KEYSTROKE GUIDE 5 Items highlighted with bullets only direct you to earlier references on the same subject. 1 Divide 5 2 Decimal 5 3 Square Root 6 4 Add 6 5 Negative and Subtract 7 6 Multiply 8 7 Divide 8 8 Exponent 8 9 Square Root 9 10 Absolute Value 9 11 Reciprocal 9 12 Negative 10 13 Fraction 10 14 Store 10 15 Alpha 10 16 Window and Default 11 17 Integer 12 18 Graph 13 19 Cursor 13 20 Enter Function 14 21 Evaluate Y 14 22 Table 16 23 Trace 17 24 Test 18 25 Zoom In 19 26 Square 20 27 Shade 20 28 Solve 22 29 Evaluate Y 26 30 Scientific 26 iv

Contents v TI-83 INTRODUCTION: On/Off, Contrast, Mode, and Editing Expressions 27 Turning the Calculator On 27 Adjusting the Display Contrast (Making the Screen Lighter or Darker) 27 Turning the Calculator Off 28 Second Functions for Keys Notation 28 Mode 28 Editing Expressions 29 TI-83 GRAPHING CALCULATOR KEYSTROKE GUIDE 31 Items highlighted with bullets only direct you to earlier references on the same subject. 1 Divide 31 2 Decimal 31 3 Square Root 32 4 Add 32 5 Negative and Subtract 33 6 Multiply 34 7 Divide 34 8 Exponent 34 9 Square Root 35 10 Absolute Value 35 11 Reciprocal 36 12 Negative 36 13 Fraction 36 14 Store 36 15 Alpha 37 16 Window and Default 37 17 Integer 39 18 Graph 40 19 Cursor 40 20 Enter Function 40 21 Evaluate Y 41 22 Table 42 23 Trace 44 24 Test 45 25 Zoom In 45 26 Square 47 27 Shade 47 28 Solve 50 29 Evaluate Y 55 30 Scientific 56 INDEX 57

TI-82 INTRODUCTION On/Off, Contrast, Mode, and Editing Expressions TURNING THE CALCULATOR ON When the ON button is pressed, you should see a blinking dark rectangle (called the cursor) in the upper left-hand corner of the screen. The screen you are looking at is called the Home screen, where basic computations are performed. If you do not see the blinking cursor, you may need to adjust the display contrast. How that is done will be described next. ADJUSTING THE DISPLAY CONTRAST (MAKING THE SCREEN LIGHTER OR DARKER) Even if your display is presently easy to view, you may find that under different lighting conditions you may need to adjust the display contrast. Also, as the batteries in your calculator become weaker with use, you will have to make occasional adjustments in display contrast. If you wish to make the display darker, press the light blue 2nd key and then hold down the Up Arrow ( ) key until the desired level of darkness is obtained. If you wish to make the display lighter, press the light blue 2nd key and then hold down the Down Arrow ( ) key until the desired level of darkness is obtained. As soon as you release the Up Arrow or Down Arrow key, the arrow keys no longer affect contrast, and you must press the 2nd key again to make the arrow keys affect the contrast. Note that when the 2nd key is pressed, an arrow pointing upward appears inside the cursor to let you know that the 2nd key has been pressed. (Why the arrow pointing upward denotes the 2nd key will be explained a bit later.) The Up, Down, Left, and Right Arrow keys are the blue-gray keys located in the upper right-hand portion of the keyboard. In many of the other uses we will have for them, they will function in the same way as the arrow keys on a computer keyboard. Experiment with the contrast setting a bit. You will find that when you press 2nd and hold down or press 2nd and hold down, a cursor with a number in it will appear in the upper right-hand corner 1

2 TI-82 Introduction of the Home screen as long as you hold down the Up Arrow or Down Arrow key. Try to adjust the contrast, and as you do, be looking in the upper right-hand corner of the screen for the contrast number. This number indicates how dark, on a scale of 0 to 9, you have made your screen, with 9 representing the darkest possible contrast setting. As the batteries in your calculator become weaker, the contrast setting usually needs to be increased to provide the same level of contrast you may have obtained at a lower setting with fresh batteries. When you need to set the contrast setting to 8 or 9 on a regular basis to see the display clearly, it is time to change batteries. When is the contrast set appropriately? To some extent it is a matter of personal preference, but there are some contrast qualities which most people find suitable. The screen is composed of tiny squares, called pixels, which darken to form the cursor, numbers, letters, etc., on the screen. Most people find that the contrast is set about right when the cursor is clearly visible and you can see that it is composed of 7 rows and 5 columns of pixels. You should also just barely be able to see where the other pixels are on the screen, but they should by no means be dark, just barely visible if you look closely. TURNING THE CALCULATOR OFF Pressing the 2nd key before pressing the ON key activates the ON key's second function, which is printed in light blue print above the ON key. Notice the word OFF written on the keyboard above the ON key. Thus, pressing the 2nd key and then the ON key turns the calculator off. If you forget to turn the calculator off, it will turn itself off after a few minutes of non-use, using the Automatic Power Down (APD ) feature. Pressing the ON key turns the calculator back on, and the screen will appear exactly as it was before the (APD ) feature turned the calculator off. SECOND FUNCTIONS FOR KEYS NOTATION To simplify matters in the future when referring to second functions served by keys, this Keystroke Guide will simply show 2nd followed by the name of the second function, enclosed in brackets. For example the keystroke sequence for turning the calculator off will be denoted 2nd [OFF]. Thus, the word in brackets is not on the key itself, but it is written above the key in light blue print as the key's second function. This is why, when you press the 2nd key, the arrow pointing upward appears inside the cursor. It is to remind you to look for the light blue print above a key, rather than what is written on the key, to determine what that key will do when you press it. MODE Before doing some basic computations, it would be a good idea to check the mode settings on the calculator which determine how results are displayed. Press the MODE key. The display should appear as shown at the top of the next page.

TI-82 On/Off, Contrast, Mode, and Editing Expressions 3 For now, it would be best to have all of the settings on each line highlighted (black background) as shown. If any of the highlighted settings on your calculator are not the ones shown above, use your Arrow keys to move the blinking cursor over the setting desired and press ENTER. Continue in a like manner until all of the settings on the left side are highlighted as shown. Press 2nd [QUIT] to return to the Home screen. EDITING EXPRESSIONS Turn on your calculator and type in 3 + 2 7. (Don't worry just yet about calculating the value of the expression.) The calculator displays 3+2*7. Note that the calculator displays multiplication with an asterisk (*). This is a common computer notation for multiplication. Entering an expression and editing it before evaluation As you can already see, the TI-82 differs from ordinary scientific calculators in more ways than just being able to draw graphs. One of its major advantages as a calculator is that it enables you to see an entire arithmetic expression as you enter it. The TI-82 also lets you easily edit the expression both before and after you evaluate it. To see how to edit, we will change the expression above, replacing the 2 with a 4. Use the Left Arrow key (<) to move the cursor until it is over the 2. Type a 4. The expression should now look like this: 3+4*7. We will now evaluate the expression. The cursor is still in the middle of the expression, but that doesn't matter. To evaluate the expression press the ENTER key in the lower right-hand corner of the keyboard. On the right-hand side of the calculator screen you should see 31 displayed, which is the value of the expression. Note that the calculator uses standard algebraic order of operations rules, performing the multiplication before the addition. Editing an expression after evaluation Suppose you wanted to evaluate 3 + 5 7. Since this expression differs from the previous one in only one character (5 instead of 4), there is a way we can quickly obtain the new expression from the old. Rather than enter the entire expression again, just press 2nd [ENTRY]. An exact copy of the last expression entered is reproduced on the screen. Now use the arrow keys as before to change the 4 to a 5, and press ENTER to obtain the value of the new expression, 38. INS (Insert) and DEL (Delete) Suppose we want to evaluate 3 + 4. 85 7. 6 by editing the last expression. If we press 2nd [ENTRY], we get 3+5*7 on the display. Move the cursor over the 5. We have one problem here that we must recognize: if we type in 4.85, we will type over part of the expression we want to keep. To avoid that, type the 4 over the 5, and then press 2nd [INS], which puts the calculator in Insert mode. Note that the cursor becomes a blinking underline. That means that the character at the cursor position and all those to the right of it will be moved to the right to make room for some inserted symbols. Type in the remaining.85 to complete the 4.85 and see how the other characters are moved to the right to make

4 TI-82 Introduction room. Now use the arrow keys to put the cursor at the end of the expression. Note that as soon as you move the cursor with an arrow key, the calculator leaves Insert mode. We are now going to change 7 to 7.6. Since the cursor is at the end of the expression, the calculator need not be in Insert mode to make this change (though it would make the change just the same if it were in Insert mode). After the 7 type in.6, and press ENTER to display the value of the new expression, 39.86. Now suppose we want to evaluate 3 + 5. 2 7. 6 by editing the last expression. Press 2nd [ENTRY] to reproduce the last expression, and use the arrow keys to place the cursor over the 4. Type in 5.2. Since 5.2 contains one less character than 4.85, the last digit of the 4.85 is still on the screen and must be eliminated. The cursor should now be resting on this last digit (5) of the old 4.85. Press the DEL key to delete this character. (Each time the DEL key is pressed, it deletes the character at the cursor position.) Press ENTER to display the value of the expression, 42.52. Next, suppose we want to evaluate 3 + 5 8. Notice that this expression could be produced by editing the last expression we evaluated, but it really looks more like the expression 3+5*7 that we evaluated some time earlier. One of the nice features of the TI-82 is that it stores as many previous entries as it can. Press 2nd [ENTRY] once to produce the last expression. Now press 2nd [ENTRY] again. Note that you now see the next-to-last expression we evaluated. If you press 2nd [ENTRY] one more time, you will see the expression we evaluated before that, which was 3+5*7. You may now edit this expression as before to produce 3+5*8. Press ENTER to evaluate it. If you continue to press 2nd [ENTRY] beyond the calculator's ability to recall previous entries, it will return you to the most recently evaluated expression. Clearing the Home screen By now your Home screen may look pretty full, and the original expressions you entered may have scrolled off the top of the screen. Any time you want to erase everything on the Home screen, just press the CLEAR key, located below the arrow keys. If you want to retrieve these erased expressions, you may still do so by pressing 2nd [ENTRY] as often as needed.

TI-82 GRAPHING CALCULATOR KEYSTROKE GUIDE As you look at the pages in your textbook, you will notice that on some pages a book icon appears with a brief description of a feature on your TI-82 graphing calculator. In this guide the page number in the textbook on which each of these book icons occurs is shown, as well as the key word or phrase which appears next to the icon, followed by a detailed description of how to use this feature on your TI-82. Each feature is also given its own number for easy reference. page 3 1 Divide The symbol appears on the division key of the TI-82, but on the screen division is indicated by the diagonal slash /. Do the division 24 divided by 6 by pressing 24 6 ENTER. Note that on the home screen the division appears as 24/6, which means the same thing, and the result is still 4. Fractions may also be entered as divisions. For example, the fraction 4 3 may be interpreted as 3 divided by 4. You may enter the fraction that way on your calculator. On the screen you will see 3/4. When you press ENTER, you will see the decimal equivalent of.75. (See also 13 Fraction.) page 4 2 Decimal Press the MODE key. Notice that on the second line of mode settings the word Float is probably highlighted. If not, move the blinking cursor over the word Float and press ENTER. Press 2nd [QUIT] to return to the Home screen. Unless the computation comes out exactly using fewer digits, when the calculator is set to Float mode, the calculator displays 10 digits, and the decimal point occurs at its appropriate place in the 10-digit display. As a result, sometimes more digits are displayed to the right of the decimal point on some computations than on others. The decimal point "floats" to wherever it should be in the 10-digit display for a given computation. For example, perform the following three divisions: 17 8, 368 7, and 9543 7. Since the computation of 17 8 comes out exactly at the third decimal place, the calculator displays only the number of decimal places needed to show the result: 2.125. The other two computations do not come out exactly, no matter how many decimal places are used, so the calculator displays ten digits and locates the decimal point where it should occur in the 10-digit display: 368 7 = 52.57142857 and 5

6 Calculator Keystroke Guide 9543 7 = 1363.285714. Notice how in these last two computations the first displays ten digits with eight of them to the right of the decimal point, while the last also displays ten digits but with only six of them to the right of the decimal point. Suppose instead that you want your calculator to automatically round computations to a fixed number of decimal places. Press the MODE key again. The second line on the Mode screen reads Float 0123456789. To make the calculator automatically round all calculations to two decimal places, on the second line of the MODE screen use the arrow keys to move the blinking cursor over the number 2 and press ENTER. Press 2nd [QUIT] to return to the Home screen. Now if you do the same three computations above again, the calculator will display the results rounded with only two digits to the right of the decimal point (that is, rounded to the nearest hundredth): 17 8 = 2.13, 368 7 = 52.57, and 9543 7 = 1363.29. When you are through making the calculator round to two decimal places, it would probably be best to return to the MODE menu and change the setting back to Float. page 4 3 Square Root The square root is the second function on the x 2 key. (Note the square root sign ð printed above the x 2 key in light blue print.) To produce a square root sign on the Home screen display, first press the light blue 2nd key and then press the x 2 key to produce its second function, the square root sign. In the future, this key sequence will be denoted 2nd [ ð ], where the second function of the key is enclosed in brackets. Other keystrokes involving the 2nd key will be denoted in a similar fashion. The expression in the brackets should be found printed above one of the keys on the keyboard. Unlike with most scientific calculators, with the graphing calculator you enter the square root sign first. To find the square root of 324, use the following keystrokes: 2nd [ ð ] 324 ENTER. On the Home screen you will see ð324. The value of this square root, 18, should have appeared on the right of the screen after you pressed ENTER. Note that the calculator only does the square root of the number immediately following the square root sign. If you want to compute 7 + 18, you must group the sum in parentheses, ð(7+18), to assure that the sum is computed before the square root is taken. (The correct value of this expression is 5.) page 11 4 Add The addition key + is on the right-hand side of the keyboard with the other basic operation keys (subtraction, multiplication, and division). Basic addition is done as it is on most other kinds of calculators: the expression containing addition may be entered just as it appears in print or when written by hand. To evaluate the expression once you have typed it in, press ENTER. For example, to evaluate 7 + 15, type this expression just as it appears and press ENTER to display the value 22. To add expressions involving negative numbers, such as 5 + ( 8), you may type this expression just as it appears, using the parenthesis keys, and pressing ENTER to obtain the value 3. Be sure you use the gray negative key not the blue-gray subtraction key when you type in

TI-82 7 the 8. (See 5 Negative and Subtract.) It turns out that you could also type in this expression without using the parentheses, and it will still work: 5 + 8 will still produce the value 3. page 11 5 Negative and Subtract You may have noticed that the calculator has two keys with a minus sign on them. The gray ( ) key in the bottom row of keys is actually the negative key. The negative key is used only to write the negative of a number. The following numbers and expressions would be entered using the gray negative key: 5 7 * 6 4 + 1 54 /( 6) The blue-gray key in the right-hand column on the keyboard is the subtraction key. It is grouped with the other keys used to perform the basic four arithmetic operations (addition, subtraction, multiplication, and division). The subtraction key is used between two numbers to indicate that a subtraction is to be done. The following expressions would be entered using the blue subtraction key: 17 8 13* 7 2 5 6(3 + 4) You can tell which of these keys has been used from the screen display, if you look closely. The negative sign produced by the negative key is one pixel (dot) shorter and placed one pixel row higher than the subtraction sign produced by the subtraction key. Be aware that it is a common mistake among new users of the TI-82 to press the wrong one of these two keys. Sometimes you will get an error message on the calculator screen when you press ENTER to evaluate an expression. Other times the calculator will do something different from what you intend. For example, suppose you wanted to do the subtraction 8 5 on the calculator. First do it the correct way with the blue-gray subtraction key and press ENTER to evaluate it. Of course, you should get 3 as the answer. Now enter it the wrong way by using the gray negative key between the 8 and the 5 and press ENTER to evaluate it. You get an error message (ERR: SYNTAX, which you can read more about some other time in the Error Conditions portion in the back of the manual which came with your calculator). What happened? The calculator does not interpret the negative key as meaning to subtract. The calculator sees this last expression as two numbers written side by side, 8 and 5, with no indication of which operation you wanted to perform on them. Therefore, the calculator doesn't know what you want done with these numbers. That's why it gave you an error message. The calculator is smart enough, however to know where the problem probably lies. Notice that with the error message you have two choices: Goto (go to the error) and Quit. Choose Goto by pressing 1 or by pressing ENTER (since choice 1 is already highlighted). The calculator returns to the Home screen with the cursor blinking on the negative sign which should have been a subtraction sign. While the cursor is there, type a subtraction sign, which will replace the incorrect negative sign, and then press ENTER to evaluate the expression. Now the problem has been fixed.

8 Calculator Keystroke Guide page 11 6 Multiply The TI-82 interprets the following as indicating multiplication: the multiplication key, numbers or expressions written side by side in parentheses, numbers and letters written side by side, and letters written side by side. If you type 3 6, the calculator will display it as 3*6. The asterisk * is a common computer notation for multiplication. When you press ENTER, the calculator will display the value 18. If you place one or both of the numbers in a multiplication in parentheses without using the multiplication key, the calculator still knows that you mean to multiply. Thus, the calculator will also produce 18 if you enter 3 6 as 3(6), (3)6, or (3)(6). Parentheses may also be used for grouping calculations to be done in a certain order. Thus, the calculator interprets 5(3+4) as meaning to add 3 + 4 first to get 7, and then to multiply 5 times the 7 to get 35. As an example of placing numbers and letters side by side, the calculator interprets 3X as meaning "3 times X." (How to enter letters will be discussed later.) To see how this way of writing multiplication works, try typing in 2π, where π (the Greek letter pi) represents that special number having to do with circles. The value of π is approximately 3.141592654. Your calculator has this special number as the second function on the caret key ^. (You should see the symbol π printed above the caret key in light blue type.) To type in 2π, type the 2 and then press the light blue 2nd key and then the caret key. (In the future we will denote these last two keystrokes as 2nd [π].) Your calculator should display 2π. Press ENTER to see the value 6.283185307, which is two times the value of π. page 11 7 Divide See 1 Divide. page 12 8 Exponent 5 The caret key ^ is used to enter most exponents. For example, the expression 2, is entered into the calculator as 2^5. Thus, the base is entered first, then the caret, and then the exponent. Press ENTER to produce this expression s value, 32. To raise a negative number to a power, it is necessary to enclose the negative number base in parentheses. For example, to raise the number 4 3 to the fourth power the expression must be written as ( 3). Likewise, we must enter this expression into the calculator as (-3)^4. The result is 81. Without the parentheses, -3^4 would (and should) be interpreted as taking the negative of 4 4 3 = (3 ) = (81) = 81. 4 3. That is, -3^4 is interpreted as Two special exponents that can be produced on screen as raised exponents are the exponents 2 2 and 3. To enter the expression 5 you could use the standard approach of typing 5^2, or you 2 2 could instead type the 5 and then press the x key. The x key produces only the raised exponent 2 on the screen, not the x. Either way, the calculator produces the result of 25 when you press 3 ENTER. To produce a raised exponent 3, as in the expression 4, first type 4 and then press the MATH key. The calculator will display the MATH menu. Choice 3 on the MATH menu is the raised exponent 3. Select it by pressing 3 (or by using the Down Arrow key to highlight the number 3

TI-82 9 and pressing ENTER). The MATH menu will then disappear, and the calculator will display 4 3. Press ENTER to display the value of the expression, 64. page 12 9 Square Root See 3 Square Root. page 14 10 Absolute Value The absolute value of a number is the number's distance from zero on the number line. The absolute value key is the second function on the x 1 key. It is denoted ABS. Thus, the keystrokes needed to get the absolute value would be 2nd [ABS]. When we write the absolute value of 7 with pencil and paper, we enclose the number within two vertical bars: 7. On the calculator the absolute value of 7 is denoted abs(-7). Produce this expression on your Home screen by first pressing 2nd [ABS]. Then open a set of parentheses, type in 7 (being sure to use the gray negative key), and close the parentheses. Press ENTER to find the absolute value of 7, which is 7. Try doing this problem again, only don't use the parentheses. You will find that when you take the absolute value of a single number, the parentheses are optional. As was the case with square roots, the calculator only takes the absolute value of the number immediately to the right of the abs symbol. To evaluate 17 + 5 we may not just enter abs 17+5, because the calculator would do the absolute value of the 17 only. We want it to do the absolute value of the entire expression contained within the absolute value bars. To do this, we must put the expression inside a set of parentheses: abs( 17+5). The result is 12, since 17 + 5 = 12 = 12. To evaluate 5 + 2 you would type in abs(-5)+abs(2)and press ENTER to obtain the value 7. To multiply the absolute value of 4 by the absolute value of 10, 4 10, you could use the multiplication key to type in abs(-4)*abs(10), or you could just put the two absolute values side-by-side with no symbol in between: abs(-4)abs(10). The calculator still knows you mean that these two absolute values are to be multiplied. The value of this expression is 40, since 4 10 = 4 10 = 40. page 21 11 Reciprocal Since the reciprocal of an integer, such as 5, may be written as 51, it may be entered into the calculator as we would enter any fraction of this type: 1/5, using the division key to produce the diagonal slash / on the screen. Similarly, the reciprocal of a fraction, such as 8 5, may be written by interchanging the numerator and denominator: 5 8, appearing as 8/5 on screen. 1 Another way to enter the reciprocal of a number is to use the x key. For reasons that will 1 be explained later, the reciprocal of 4 may be written as 4. To produce this expression on

10 Calculator Keystroke Guide 1 screen, press 4; then the x key, which produces only the exponent 1, not the x. Press ENTER to display the value of the expression,.25, which of course is the decimal equivalent of 1 4. page 27 12 Negative See 5 Negative and Subtract. page 35 13 Fraction Fractions may be entered into the calculator by using the division key to produce a diagonal slash fraction bar. The TI-82 can perform operations on fractions and give answers in either decimal or fraction form. Enter the expression 5 1 by typing 5 6 1 2. The expression will 6 2 appear on the Home screen as 5/6-1/2. Press ENTER to get the decimal form of the value of this expression (approximately.3333333333). If you prefer to get your answer in fractional form, you must do one extra thing before pressing ENTER. To see how to get a fractional answer, either type in the original expression again or use 2nd [ENTRY] to reproduce it on the Home screen. With the cursor at the end of the expression, press the MATH key. Choice 1, which is already highlighted, is Frac, which converts the preceding expression to fractional form, if it can. Press 1 or ENTER (since choice 1 is already highlighted). The display will return to the Home screen, where the fraction conversion symbol will appear after the expression: 5/6-1/2 Frac. Now press ENTER to see the fractional value of the expression (one-third). page 73 14 Store The STO> key is used to store a particular number value in a variable (letter). That is, it assigns a specific numerical value to a letter. If you wish to make the letter B represent the value 7, then you must store the value 7 in the letter B. To do this, first type the number 7 and then press the STO> key. Notice that an arrow appears on screen next to the number 7. To type the letter B (or any other letter) first press the ALPHA key. Note that the cursor has changed: there is a letter A inside the cursor, which indicates that the calculator is in Alpha mode. You may have noticed that letters of the alphabet appear above many of the keys on your calculator. When the calculator is in Alpha mode, as it is now, and you press one of these keys, it produces on screen the letter of the alphabet shown above the key, rather than performing its usual function. Since you want to store the value 7 in the letter B, press the key that has the letter B printed above it: the MATRX key. Your screen should now show 7 B. The calculator doesn't actually store 7 in the letter B until you press ENTER, which you should do now. From now on, until you change the value stored in B, the calculator assigns the value 7 to the letter B. Even turning the calculator off won't erase this result. To type in 3B, type 3 and then press the ALPHA key to put the calculator into Alpha mode. (When you do, the letter A should appear inside the cursor.) Then press the MATRX key, which has the letter B printed above it. Press ENTER to display the value of 3B (3 times B), which is 21, since 3B = 3(7) = 21. page 82 15 Alpha To type letters of the alphabet, which are printed above many of the keys, the calculator must be in Alpha mode. To put the calculator in Alpha mode for one keystroke only, press the ALPHA key

TI-82 11 and then press the key that has the desired letter printed above it. When you press the ALPHA key, the calculator lets you know it is in Alpha mode by displaying the letter A inside the cursor. (If the calculator is also in Insert mode because 2nd [INS] was pressed first, the Insert mode underline cursor will have an A printed above the underline.) For example, to produce the letter P on screen, press the ALPHA key to put the calculator in Alpha mode and then press the 8 key, which has the letter P printed above it. Notice that after you press the 8 key, the calculator is no longer in Alpha mode. If you wish to type several letters in succession, the calculator may be locked in Alpha mode by pressing 2nd [A-LOCK]. Try using this feature to spell the word CAVE. Press 2nd [A-LOCK] and then type in the four letters as they are found above the keys. Notice that the calculator stays in Alpha mode the entire time. To escape from Alpha mode, press the ALPHA key again. The A should disappear from inside the cursor. (If you had pressed the ENTER key, the calculator would also have left Alpha mode.) You may have noted the unusual Alpha character written above the zero key: ς. It represents the spacebar. This character does not show up on screen, but rather this Alpha character produces a blank space on screen. page 86 16 Window and Default The WINDOW screen lets us determine which part of the coordinate plane will be displayed on the calculator when a graph is drawn. The part that is displayed is sometimes called the viewing rectangle or graphing window. The default viewing rectangle, which on your calculator is called the Standard window, is a graphing window in which the displayed values of x and of y vary from 10 to 10, with tick marks (little scale markings on the axes) occurring one unit apart on both axes. There are two ways of setting your calculator to this Standard (default) viewing window. The first is to set it manually. Press the WINDOW key. The Window settings displayed may be changed by using the arrow keys to move the cursor to the proper line and by typing over the existing values. The first number, denoted Xmin, represents the smallest value of x to be displayed on the graphing window. Xmin indicates the value of x at the extreme left edge of the graphing window when it is displayed. On the Standard (default) viewing window Xmin = 10. Xmax represents the largest value of x to be displayed on the graphing window. Xmax indicates the value of x at the extreme right edge of the graphing window. On the Standard (default) viewing window Xmax = 10. Xscl indicates the distance between tick marks on the x-axis. On the Standard (default) viewing window Xscl = 1. Ymin represents the smallest value of y to be displayed on the graphing window. Ymin indicates the value of y at the very bottom of the graphing window when it is displayed. On the Standard (default) viewing window Ymin = 10. Ymax represents the largest value of y to be displayed on the graphing window. Ymax indicates the value of y at the very top of the graphing window when it is displayed. On the Standard (default) viewing window Ymax = 10. Yscl indicates the distance between tick marks on the y- axis. On the Standard (default) viewing window Yscl = 1. In summary, when you have set the Window settings to the Standard (default) values, the screen should display the following: Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1

12 Calculator Keystroke Guide To see this Standard (default) viewing window for graphs, display the Graph screen by pressing GRAPH. Your screen should display a graphing window like the one shown in Figure 2.10 on page 86 of your text. To see another graphing window, press the WINDOW key, change the settings as shown below, and then press GRAPH again to see this different graphing window: Xmin=-4 Xmax=12 Xscl=2 Ymin=-50 Ymax=80 Yscl=25 The left edge of the screen is at x = 4, and the tick marks on the x-axis are 2 units apart, so the first tick mark to the right of the origin on the x-axis represents 2, the next one to the right of it represents 4, the one after that 6, etc. On the y-axis the mark at the very bottom of the screen represents 50, and the tick marks on the y-axis are 25 units apart, so the first mark above the origin on the y-axis represents 25, the next one above it represents 50, and the next represents 75. Since the value of y at the very top of the screen is 80 (Ymax), notice that the y-axis extends just a bit above the tick mark representing 75. There is a second way to produce the Standard (default) viewing window on your calculator. Any time you wish to return the Window settings to the Standard (default) settings, just press the ZOOM key and press 6 to select the Standard viewing window (ZStandard). (From now on, this keystroke sequence will be denoted ZOOM 6.) The graphing window will then be displayed with the Standard (default) settings. To verify that the calculator has changed the Window settings to the Standard (default) values, press the WINDOW key to view the settings. Any time you wish to return to the Home screen from any of these other screens, just press 2nd [QUIT]. page 86 17 Integer Sometimes we want to have a graphing window that will display integer coordinates, rather than the lengthy decimal coordinates that often arise with other graphing windows. Such a viewing rectangle is called an Integer graphing window. Although an Integer graphing window may be produced beginning from any set of Window settings, press ZOOM 6 to display the Standard (default) viewing window. Press the ZOOM key once more. Notice the arrow pointing downward at the bottom of the screen next to choice 7. That arrow indicates that the Zoom menu has more items in it which may be viewed by pressing the Down Arrow key to scroll the menu downward. Press the Down Arrow key several times (or hold it down) until the highlight is on 7. Now press the Down Arrow key once more. Notice that the menu has scrolled downward to reveal a choice 8, which is ZInteger. Choose ZInteger either by pressing 8 or by moving the highlight to 8 and pressing ENTER. The calculator will display the as-yet-unchanged graphing window, and there will be a set of coordinates displayed at the bottom of the screen which represent the coordinates of a small free-moving cursor, which may be a bit hard to see, since it is at the origin. (You may see a blinking pixel at the origin.) Press the Up Arrow and Right Arrow keys a few times so that

TI-82 13 you get a better look at this free-moving cursor. This cursor should be moved to approximately the coordinates of the point you want to have in the center of the screen after the calculator creates the Integer graphing window. If you wish to have the point (7,5) at the center of the Integer graphing window, then move this free-moving cursor to a point as close to (7,5) as possible. That is, move the cursor with the arrow keys until the coordinates displayed at the bottom of the screen are as close as you can get them to x = 7 and y = 5. (From the Standard graphing window, the closest you can come is probably x = 7.0212766 and y = 4.8387097.) Press ENTER to produce the Integer graphing window centered at (7,5). Press the Right Arrow key to produce a larger freemoving cursor one pixel to the right of the center of the screen. (See 19 Cursor for more details about this cursor.) Note that the coordinates of the cursor are (8,5). Press the Left Arrow key to return to the center of the screen, which is at (7,5). Press other arrow keys and note that every time you press the Left Arrow key or the Right Arrow key, the value of x remains an integer and changes by 1. Likewise, every time you press the Down Arrow key or the Up Arrow key, the value of y remains an integer and changes by 1. You may want to look at the Window settings to see how things have been changed. Press the GRAPH key again to display the graphing window. If you want to change the coordinates of the center to some other point, such as the origin (0,0), press ZOOM 8, move the cursor to (0,0), and press ENTER. A new Integer graphing window will be produced, this time centered at the origin. Use the arrow keys to verify that this change has taken place. page 86 18 Graph See 16 Window and Default first to learn how to set the left, right, bottom, and top of the graphing window with the Window settings. To see the graphing window you have selected, press GRAPH. page 87 19 Cursor Press the GRAPH key to display the graphing window. (It doesn't matter which graphing window you are using, nor does it matter if graphs are displayed.) Press one of the arrow keys. (It doesn't matter which one.) You will notice that near the center of the screen there is a cross hair, and at the bottom of the screen there are values for x and y which represent the coordinates of the cross hair. If you cannot see the cross hair clearly because it lies on one of the axes, press the Up Arrow key a few times and the Right Arrow key a few times to get the cross hair away from the axes. You may notice that when you do this, the coordinates displayed at the bottom of the screen change to reflect the changed position of the cross hair. This cross hair may be moved to any part of the graphing window by using the arrow keys. The cross hair is sometimes called the general cursor or free-moving cursor. To turn this general cursor off, just press the GRAPH key.

14 Calculator Keystroke Guide page 92 20 Enter Function See also 16 Window and Default and 18 Graph. To graph an equation, to use an expression repeatedly for computations, or to generate a table of values of an expression (See 22 Table.) such as 2x 3, the expression first needs to be entered in the Y= screen. First press the Y= key and erase any old expressions by placing the cursor on the expression to be erased and pressing CLEAR. Then type 2X 3 to the right of the equal sign next to Y1. The easiest way to produce the letter X on the screen is to press the X,T,θ key. To see the graph of this equation, just press the GRAPH key. The graph will be displayed on the graphing window with the Window settings you selected. (Refer to 16 Window and Default.) Using the Standard viewing window, you should see the graph of a straight line as shown below. Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 You may graph up to ten equations on the same graphing window, using the Y= screen to define the equations to be graphed. (There are ways to produce more than ten graphs on the graphing window, but we won't discuss that here.) For example, press the Y= key, keep Y1=2X 3, and move the cursor down to the right of the equal sign for Y2 and type X 2. (Use the x 2 key to produce the exponent 2.) Thus, you are defining Y2 to represent y in the equation y = x 2. To graph both of these equations, press the GRAPH key. You should see the same straight line as before, representing the graph of Y1, and you should also then see the graph of Y2, which is a curve that lies almost entirely above the x-axis. It just touches the x-axis at the origin. Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 If you return to the Home screen or turn the calculator off and then back on, the graphs will still be there to view by pressing the GRAPH key. The graphs will also automatically be displayed if you press ZOOM 6 to display the Standard (default) viewing window. page 92 21 Evaluate Y You can use the Store command to help you evaluate an algebraic expression involving the variable x. (See 14 Store.) All you need to do is enter the expression on the Y= screen as Y1 (or

TI-82 15 any one of the ten y's in the Y= screen), store the desired value in X, and ask for the value of the variable Y1. How to do all of this is perhaps explained better by looking at the following example. On the Y= screen enter y = x + 4 as Y1, that is, Y1=X+4. Press 2nd [QUIT] to return to the Home screen. To get the value of this y when x is 6, store 6 in X (see 14 Store) by pressing 6 STO> X and then ENTER. Now all you need to do is ask the calculator for the value of Y1. To do this, first press 2nd [Y-VARS]. Next press ENTER to choose the Function... menu. Choose Y1 from this menu by pressing 1 (or ENTER, since Y1's number is already highlighted). Y-VARS menu Function menu The calculator returns to the Home screen, and the variable Y1 will be displayed on the screen. Press ENTER to find the value of Y1 when x = 6. The calculator should display the value 2. (Check the result with pencil and paper.) To find the value of Y1 when x = 4, store 4 in X, display the variable Y1 (Try pressing 2nd [ENTRY] a couple times to bring Y1 back on the screen instead of going through VARS again.), and press ENTER. Try this same approach to find the value of Y1 when x is 0, 2, and 5. The answers may be found in Example 1 on page 93 of your text. On the TI-82 there are other ways to evaluate an expression. One way relates the results to the graph. Graph the equation y = x + 4 mentioned above, using the Standard viewing window (Zoom 6). Press 2nd [CALC] to display the Calculate menu. Press 1 or ENTER to choose the value command. The Graph screen is displayed, and at the bottom of the screen appears Eval X=, followed by a cursor. Type in the value of x you want, such as 6 in the example above. When you press ENTER, the coordinates of the point on the graph where x = 6 appear at the bottom of the screen: X=-6 Y=-2, and a cross cursor appears on the graph to indicate where that point is. If you have more than one graph drawn, press the Down Arrow key to see the values of y for the other equations at the given value of x. See 22 Table for still another way to evaluate a Y variable for any desired values of x.

16 Calculator Keystroke Guide page 92 22 Table The TI-82 graphing calculator has a TABLE feature, which constructs a table of values of the variable X and the corresponding values of the Y-variables. In the Y= screen enter the expression 2 x + 3 as Y1. Now press 2nd [TblSet] (the second function of the WINDOW key). You should now see the Table Setup screen, as shown below. Suppose you want the table to begin with the value x = 3. The cursor should be on the TblMin line. Type in 3 and press ENTER or use the down arrow key. The cursor will then go to the Tbl line. Tbl is the amount by which x will change as you move from row to row in the table. Suppose you want the value of x to change by one (1) as you move from row to row. Type in 1 (if that is not already the value). Both the Indpnt and Depend settings should be on Auto. The Table Setup screen should now appear as it does below. Now press 2nd [TABLE]. (TABLE is second function on the GRAPH key.) The calculator should display a table of values of x and Y1, as shown below. The highlight is now on the initial value of x, which we had decided would be 3. Press the Down Arrow key until the number 3 is highlighted. Now watch the screen as you press the Down Arrow key once more. Note that the table has "scrolled" down one row: the old first row no longer appears, all the other rows have moved up one, and a new last row (where x is 4) appears. Press the Down Arrow key again to make the table scroll again. Try it a few more times. Try holding down the Down Arrow key for a few seconds to see how the table continues to scroll downward

TI-82 17 through larger values of x. Press the Up Arrow key until the top number is highlighted. Now watch the screen as you press the Up Arrow key once more. Note that the table has scrolled up one row. Press the Up Arrow key again to make the table scroll up again. Try it a few more times. Try holding down the Up Arrow key for a few seconds. Note that the screen scrolls upward. The first value of x we used was 3. You can scroll back to that starting point by using the Up Arrow key. Note that if you get 3 to be the top number in the X column, you can continue to press the Up Arrow key and have the table scroll up, showing more negative values of x. Any time you want to leave the table and return to the Home screen, just press 2nd [QUIT]. There is yet another way to evaluate an expression on the TI-82 for your own list of values of x, using the Table feature. Press 2nd [TblSet ] (the second function on the WINDOW key). Ignore the values of TblMin and Tbl for now, and use the arrow keys to move the blinking cursor to the line headed Indpnt. Move the cursor over the word Ask and press ENTER. On the line headed Depend move the cursor over the word Auto and press ENTER. Now press 2nd [TABLE] (the second function on the GRAPH key) to display a table. Type in any value of x you want, such as 3 in the example above. Press ENTER to see the value of Y1 (and any other Y's you may have) displayed in the table. Choose any other values of x you want and use the same procedure to evaluate your Y-variables. page 94 23 Trace When you have displayed a graph of an equation, you may trace along points on the graph by using the Trace cursor. For example, clear out any old equations from the Y= screen and enter as Y1 the expression x + 4. To get an Integer graphing window (see 17 Integer) on your calculator which corresponds most closely to the graphing window shown in Figure 2.18 on page 94 in the text, first press ZOOM 6 to get the Standard (default) viewing window. Then press ZOOM 8, and with the cross-hair cursor still near the origin, press ENTER to create the desired Integer graphing window. (You may want to look at the Window settings to see that they are similar to but not exactly the same as those shown in Figure 2.18, which are for a different calculator model.) To activate the Trace cursor, press the TRACE key. A cursor will appear on the graph of the equation, and the coordinates of the cursor will appear at the bottom of the screen. To move the cursor along the graph and display the coordinates of other points on the graph, use the Left and Right Arrow keys. Unlike the general cursor (see 19 Cursor), the Trace cursor always stays on the graph and displays only coordinates of points which are on the graph. To turn the Trace cursor off, press GRAPH. If more than one graph is displayed, the Trace cursor may be made to trace along each graph listed on the Y= screen. For example, go to the Y= screen. Keep the expression already entered as