TI-83 or 84 Tips - 932 Appendix B Keystroke Guide for the...

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Unformatted text preview: 932 Appendix B Keystroke Guide for the $83184 Calculator Series Figure 8.1.2 The key accesses the blue function above each key on the Tlu84. The ALPHA key accesses the green letter or character above each key on the 11—84. The MATH key brings up a menu with various mathematics! functions. , is appendix is designec to help you effectively use your Tir83 or Tl—84 series, 33,; culator to explore the mathematical ideas and applications in this textbook. Th 5 keystrokes for both the Ti-83 and ~“~84 families of calculators are the same. on“; the colors of the keys differ. i Review Sections 8,143.4 to learn about the basic operations you can perform on your call oclator, especialiy if you are a new user. These sections ate prerequisite to the later materiag in the appendix, which shows specific keystrokes for correspondingexamples in the textbook Keystrokes are'grouped by main topics, such as "graphing functions" or "solving eqiiations‘" Today’s calculators have many features, and so there is often more than one way to work a problem. Most of the keystrokes in this appendix illustrate only one technique, but! you shouid feel free to expiore other ways to accomplish the same task. ,...».v IMWBW “m. “ “it-WW. Mm- The row of buttons jest beicw the screen is used to create graphs and tabics. See Fig“ ure 13.1.1 {taken from the T164). l Figure 8.1.1 I i E r A second set of keys is used for navigation and to access various mathematical func— tions. See Figure 18.1.2. On the TI~84, blue is used for the function keys. On the T383, yeilow is used for the function keys. Arz'ow keys move the cursor on the screen, Throughout this appendix, the keystrokes corresponding to the functions above a key Wilt be denoted by 2&0 [KP/{Name of function above key)] . For example, the keystroke for the CALCULATE menu wilt be given by -. Initializing Your Caicuiator Calcuiator 0n/0ff Tom the calculator on with the buttoniTurn the caiculatc>r 0J5: with the button. Section B. 21:“ .«sGetting Started 933 Home Screen When you turn the calculator on, the Home Screen is displayed. This is where you enter expressions and instructions to compute numeric resultsYou can always get to the Home Screen from another window mode by pressing -. Press to clear the Home Screen. The Cursor A blinking box called a cursor determines the current position on the screen and 1s moved around by the arrow keys. Changing the Screen Contrast Press and the up arrow key to make the display 5‘ - darker or ress -?.No and the doWn arrow ke to make it 15 hter. toasters ’ p y g SEQUENTll-‘l , . , , _ , ‘ , _ Initializing the MODE In the MODE menu, accessed by pressrng -, highlight the first entry in each row unlessdirected to do otherwise. See Figure 8.2.1. Press to exit the MODE menu. Arithmetic Operations Calculations -Key in the expression in the Home Screen and then press -. The standard arithmetic operation symbols are used. Subtraction Symbol and Negative Sign These are dijj‘erem keys. To enter a negative number, use . This key appears directly beneath the 3 key. To subtract, use E], directly above the key. Order of Operations Working outward from the inner parentheses, operationsare performed from left to right. Exponentiation and any operations under a radical sym— g bol are evaluated first, followed by multiplications and divisions, and then additions iii; and subtractions. If you want to change the algebraic order, you most use parentheses. Parentheses also must be used around the numerator and denominator in fractions. See Section Al for more information. fii‘ ' he j’i W. i? Evaluating Simple Expressions ' mum. —.—-a-;vw..~<:wn7:v F‘E' .1: mm- :Y‘Luzo .n».- .v. on: mew-new.» Use a calculator to evaluate the following. (a) 2 + 4 - 5 m 3 5 + 4: (b) 1 ~i- 2 a» Solution (a) Press 2 4 S E} 3. The answer is 19. See Figure 32.2. (b) Press 5 4 [E] I 2 .. The answer is 3. Note that the numerator and s denominator must be entered using parentheses. See Figure 3.2.2. as Menus and Submenus The TI—83 and TI—84 Plus operate using menus and submenm.%en you press a menu key such as on the calculator, the submenus are listed in the top row of the screen. The highlighted submenu is displayed. Use the right and left arrow keys to move to {he other submenus. To exit a menu, press MODE (QUIT) .The following example shows how to access a menu or submenu item. iii 934 Appendix B a? Keystroke Guide for the Tl—83/84 Calcoiator Series Change 3184—9 into decimal form using the MATH menu. Es~$eieizion There are two ways to access a MATH menu item. Use whichevg; YOu fer.The keystrokes in this appendix use Method A to access menu items. ' Method A Use a numeer to select the menu item. Enter 49 Q 8 on the H Screen. Press and then 2 for E whee. Fress - The ans w6.125. See Figure 13.2.3. ' Method 3 Use an arrow key to select the menu item. Enter 49 E3 3 on the " Screen. Press and use the down arrow key to move to a : )99c P --.The answer is -6.125. F”? The following explains how to edit entries in the command line. Change the Current Entry Move the blinking cursor to the current entry and typ _ the new entry, which replaces the old entry. Delete the Current Entry Move the cursor to the character and press -. Insert a New Entry Move the cursor to the character after the insertion point press DELGNS) to type in new text or symbols. Edit a Previous Entry In the Home Screen, press to recall the laws entry, and edit it as explained above. You may continue to press EN‘i'ER (Enter) I recall even earlier entries. I Clear Data To complezeiy delete data from memory, press] and th 2 for E = Delete and delete from any of the given menus. Press exit the rnenu‘. M wmmM'ExreS—vns Expressions can be entered on the Home Screen or in the equation editor by 13156? the editor. Expressions that can be readily evaluated are usually entered on-th Home Screen. Order of operations always applies, so you must use parenmeses 1f wish to change the order. See Section A31 for details. ‘. Your calculator contains many built—in functions, such as LN and 835- Bl“ functions can be accessed via the keyboard, the various menus, or the Catalog: W. is a menu containing an alphabetical list of all functions. When using built-in tions, 3 left parenthesis is often included so that you only have to enter the inpat val and then type the right parenthesis to complete the expression. The following table iliustrates various examples of entering expressionsYou. not yet have studied the expressions for numbers 844, but you can come back {0' as needed. ; Section 3.41s Entering and Evaluating Common Expressions 935 1 . Rational expression 2. Change decimal to fraction 0.5 ; press 1 for I: =>Frac 3. Absolute value 15! -63; press 1 for 3; = abs< and then press 5 and . Square root -/1 ‘2' 12 . Root from MATH menu \57 16 4-; press 5 for 5 =\’7 and then press 16 R00: from Home Screen V4 16 16.1 E} 4 .Square ‘ 62 ‘601’62 . Power -.7 . Natural exponential function 3 9. Natural logarithm ln(x - 2) I B 2 10. Common logarithm log(x + i) 1 :11.Logarlthm tobaseb loggx .--."“2 (use change—of—base formula) 12. Factorial ‘ . 7-."5press 4 for 1H5 l3. Combination 804 8 .[E] ,- press 3 for 3 = nCr and then press 4 14. 1’ermutation ‘ SP3 8 E] E} El; press 2 for BMW and then press 3 15. Scientific notation 3 X 104 3 4 Evaluating Variable Expressions You can store the value of a variable and then use it to evaluate expressions. From the Home Screen, you can assign the variable any name from A to Z. we ' ,3. Evaluagifpgwan Expression Cont ining One Variable ~-' mrmr. Assign the value of w 1 to the varia’oie A and evaluate 2A2 + 4A ~ 1.Then evaluate the expression for A w 3. leeEsia’tiaa Access the Home Screen. 1. Store the value of ~1 by pressing 1 A-. 2. Borer the expression as follows: 2 A 2 [3 4 A B 1 -. The calculator will display the answer of ~3. See Figure 8.4.1. 936 Appendix B is Keystroke Guide for the Tiu83/84 Calculator Series 3. If you want to evaluate the expression for A = 3, store the value of 3 in A as {0110‘ 3 "A. Now recall the variable expression by pressing @ ENTER (ENTRY) ENTER .The answer is 29. See Figure B4,}. ;.3 You Can also evaluate expressions containing more than one variable. - :3, Evaluating an Expression ContainingManyVaz-iahlas I ‘ Engagementvetxylmwmssrrxmnwmn‘m:”mm-meowHannah. . A 4" 2B2 1 Evaluate the expressmn T for A = —2, B = 1, and C m 5‘ fieSelurion l.Assign a value to each variable: . ; . IZWAWBE} lemme . Figure .142 Only the value of C is displayed, but the other values will be stored in memOIy.The i ., colon allows you to enter muitiple statements On one iine. 2. Enter the expression: w ALPHA A[i]2 ALPHA BQZ”@3C._ The answer of 0 is displayed. See Figure 13.4.2. The fractional expression must be entered using parentheses to separate the numerator and denominator. You can change the values of the variables and reevaluate the expression as shown in the previous example. % Using the CATALOG Function The CATALOG function, the function above the 0 key, is an alphabetic list of ali the Figure 3,4,3 functions and symbols available on the calculator. Most of themqare in a menu or on the keyboard, but you can use the CATALOG when you forget which menu you need. 3 Using the CATALOG _ .. . f .{vl Wmummm-mmmrmmmmmnmrmwctmmmmmw. A": at union? Use the CATALOG to convert‘0.125 to a fraction. ie$nlution 1. Enter 0.125 on the Home Screen: 0.125. 2.Press GlCATALOG). Since you want to convert to a fraction, your filflCEion begins with the letter F. Press -. You do not need to press or because the CATALOG is set up to directly accept alphabetical input. Use {9 scroll to the command IvFrac. 3. Press . The answer 1/8 is displayed. See Figure B43. m 5 Enterin and Evaluatin Functions ...... . WW You must enter functions into the Y: Editor in order to generate tables and graph-‘3- Once the function is entered, it can be evaluated at different values of the input variable. 1 When defining a function in the Y: Editor, only X is allowed as the input variable. if your function uses a different letter for the input variable, you must rewrite the 5135’ _:_ tion in terms of X before entering it into the Y2 Editor. Section 3.6.1:. Building a Table 937 1 Evaluating a Function . mmw Wmlu A‘mwlwr warm-M1; 15r- m1 Enter the function f(x) = x2 + 2 and find f(3) and f(— 1) regulation 1. Press to access the editor. In theY= Editor, enter the definition for Y1 as follows: 2 2. Note that the equal sign is highiighted. See Figure 13.5.1. 2. To evaluateY1(3): j (a) Press to return to the Home Screen. (b) To access the functionYi, press and use the right arrow key to highlight ‘ the Y - VARS submenu. ; (c) Press '1 to access the FUNCTION menu and press 1 for the function“. This is the oniy way to access any named function. (:11) You will now be on the Home Screen showingYi. Compiete the expression by typing 3 . The answer, I1, is displayed. See Figure 3.5.2. Figure 3.5.2 3. To evaluate Y1(- 1), press to recall the previous line. Move the cursor to highlight 3, delete it, and repiace it with 1. Press to get the is answor, 3. )fl Aitemate Method Enter the function as in Step 1.You can use the TABLE menu in ASK mode to evaluate a function. See Section 13.6 for details. iii-i Selecting and Daselecting Functions in the Y: Editor Move the cursor to the equal sign and press -. When the equal Sign is highiighted, the function is'seiected. When it is not highlighted, the function is not selected. You can enter more than one function in the Y: Editor. Figure 13.5.3 shows two functions entered in theY= Editor. on @ Deleting Functions in the Y: Editor Move the cursor to the right of the equal sign of the function you wish to delete. Press -. 31% Buildin “*WM mm To create a table of values for a function, use the commands GRAPH (TABLE) and WINDOW {TBLSET} .The function must be entered using the Y3 Editor. ' E. Generating a Table Automatically ' - -':. .v..- .mwazwr‘ww-«v W"*mmobr-.!‘JJ:1’.:V:“JVAF. .1».- Display a table ofvalues forf(x}= —x - 2, x m» MS, Mi, w3, 938 Appendix B e; Keystroke Guide for the Ti—83/84 Calculator Series iéefieluiion 1. Press and enter the function as Y1: 2- 3 E3 2. See Figure 13.6.1. 2. Press —. Fili in the following: ix Tolster'tfl S; nTb1= 1 "2 Highlight A u t o for both E n d p n t = and E) e p e n d : options. This sets the beginning X value and the change in each X. value. The highlighted A uto option for the in» ciependent variable will automatically generate the X values. ‘ l Press -. See Figure 13.6.2. Figure 3.8.1 Figure 8.6.2 Generating tables sea. - Figure 3.6.3 1;: , 4‘ 2 Generating a Table , "- inmvmrnznmmwummmzfimh.r.new: seSelonon 1. In rheY= Editor, enter the function as Y1. See Figure 33.6.3. 4 El 2.1311333 -. Fin in the following: 32v Tslstartw 5; nTb1= 1 Le Highiight Ask for Indpnt and Auto for Depend. The Ask option for the independent variable is highlighted to manually generate the X values. See Figure 13.6.4. 3. Press GRAPH (TABLE) .The table is displayed with. no entries. Move she cursor to the first entry position in the X input column to enter the X values. Press M510-2m34- As each input value is entered, the corresponding output value appears in [he Y1 column. See Figure 36.4. BEE .9? —. if; 12"? €92,332}!!! $.54 Section B 7 is" Graphing Linear, Quadratic and Piecewisewiliefined Functions 939 To graph 3 function on a calculator, first enter the function in the Ym Editor. Then choose a window setting by specifying the minimum and maximum vaiues of x and y. You can use a table of values to help you determine these values; Window settings are abbreviated as {)(max, Xmin] (Xscl) by [Ymaxflmin] (Yscl).Xsc1 andYsci define the distance between the tick marks on the x»- and y-axes, respectively. If Xsci m 1 or Yscl = 1, these values wiil be omitted from the keystroke sequence. 1E. Graphing. a Function mw‘flmmm‘“*r"h~ mienwsmmee-m Aw Wfl‘t =:\vv.wv. w- v 2 Graph y = 3x — 2 by using a table of vaiues to choose an appropriate window. eeSeiutios 1. Enter the function. Press a .I “2 . 3) I m -E] 2 to enter the function asYi in the equation editor See Figure B 7. i. 2. Generate the table. Press- m m —and fill in the following: Tbl st a r 1:: m5; n'?bl= 1; highiight Auto for both Inclpnt: and Depend: and press m. See Figure B 7.2. 3. Scroii through the table. The function crosses the x-«axis at (3, O) and the y axis at (0; —2). These vaiues must be displayed in the Window A window size of [— —7, 7] by [m7, 5] will show the x- and y—intercepts and also give a good View of the graph. Other choices are aiso possible. 4.}Enter the window dimensions by pressing ‘. Then set Mint-7, )(rsaxa 7, Xsclz 1 and Ymin= 7, Ymaxi 5, Ysc1= 1. Press -.The graph in Figure 3.7.3 is displayed. Figure 3.7.2 Figure 3.7.3 You can also graph 3 function by using built—in window settings accessed from the ZOOM menu.This will be discussed in the following section. 33 Built- -in Window Settings .- swam-mm; unwise .‘w \‘JCL. "rm-"W1 Graph the lines y = —2x + E and y = 2x - 7 using the decimal. standard, and square . . 3 2 Window settings. is Sciatica LPIessflandenterQZQL’om.183mer1. 2. ForYz, enter 3 [3 2- m E] 7m. 42w 940 Appendix B 22.22; Keystroke Guide for the TI—83/84 Calculator Series 3. The keystrokes for each type of window are summarized in the foliowing table F, t _ . . . .. .... - , “1:? Press and then 6. ' . Press and then 5. 10 10 —-lS.l6 ~3.l -10 The lines look perpendicular. The lines do' not look The lines look perpendicuiar. ' The units on both axes have the perpendicular. The units on each The units on both axes have the same size. However, the window axis have different sizes. same size. size is not big enough. To see the true shape of a circle, an eilipse, or any other figure, you will need to use a decimal or a square window. i152; 11:1} Graphing a Quadratic Functionwm‘"U__‘_ _ . - WN155-wwwku—wamw: v<iir1tu4nefiflr\ w. m.:1.:1 v Graph the function f(x) m x2 + x w 12. lie-Solution E. Enter the function as Y: in the equation editor by pressing {H [X1 T. 9. diflifl [x.T. e. n] [w] 12. If you simply press 6 to graph in a standard window, you wili not obtain a Figure 8.7.4 complete picture. Part of the parabola will be cut off. See Figure B14. Since the graph of this function is a parabola, the vertex should be visible on your graph. 2. Generate a table of values to help you locate the vertex. Press and fill in the foilowing: 'i‘blstar‘t: 10, Mble 1, highlight Auto for both Indpnt: and Dependi. Press _ Refer to Section 3.6 for more details. Scrolling through the table, you can see that the Y1 values decrease untii X = 0 and then start to increase. The vertex is near the point (0, W12). See Figure 3.7.5. 3. Press and enter window settings such as [— 10, 10} by [— i4, 10] or some» thing Simii at. See Flgure 13.7. 6. 4. Press and a complete graph 13 displayed. See Figure B. 7. '1‘. Figure 8.7.5 Figure 8.7.8 Figure 8.7.7 Figure 8.7.9 mials, Ratoinal Functions, and ine- Section 3.8 Graphing Polynomials, Rational Functions, and inequalities 941 ie w e-Defined Function . um: 411w. é: Graphing a mmnammm.mnms:mmau 3, < 1 Graph the piecewisendefineé function HCx) = { x . l + x, x a 1 isfiolstion 1. Assign a ciifferent name to each piece of the function in theY= Editor and state the x values for which each piece is defined. In the Y: Editor, enter Y2=3l---- Press 5 to choose 5 : <. Then enter 1.- EnterY2= "-u-I --. Press 4 for M2. Then enter 1.. See Figure 13.7.8. 2. Press 6 to get the graph. See Figure 3.7.9. 3. At x =. 1, the function jumps from *3 to 2, and the screen may show a line connectw ing these values/This is not part of the actual graph. To keep the calculator from con— necting across the jump, press and set the mode to DOT. Now press -. See Figures 13.7.10 anti 13.7.11. Figure 8.7.18 Figure 3.7.11 W10 MIG Est To describe an interval such as 1 :3 x S 3 for a'piecewisewdefined function, you must rewrite the interval as x E I and x S 3.To enter and, press MATH WEST) and select the LOGIC submenu. Press 1 for 1. z arid. uaities For more complicated functions such as poiynomials, you may have to try a few window settings before you get a reasonable View of the graph. x :5; Graphing Poly I‘M canyon-smnmmummmcm» .. Graph the function f(x) ~ (x — (3)30: + a)? isngsiiniss 1. In the Y: Editor, enter II-IE363I-III22 2. Since this polynomiai has zeros at x W 6 and x m “2, choose Xmin and Xmax so that the zeros lie between them. Press and choose the settings [—«4, 8] by [m 20, 10]. Press -. Note that a part of the graph is cut off. See Figure 13.8.1. .bs fifi$fi>¢m$nwvmlfi a:===‘. #15215 .55". ZE‘Efifiififif‘? fi"“/( . . M. fifi.§:‘i 942 Appendix B Keystroke Guide for the “ii—8384 Calculator Series Figure 3.8.4 3. Press and press 0 for E1 : Zoom Fit to fit the 3; values. Now you can see ,' zeros and the end behavior of the function. See Figure 8.8.2. Lu 4. To get a better view of the middie portion of the graph, press and Set Ymint 2900, max: 2000,Ysc1= 500 and press -.The graph 31mm. ' Figure 13.8.3 is displayed. The zeros, end behavior, and shape of the graph bemeés. . the zeros are now visible on the screen. a Figure 8.8.2 Figure 3.8.3 800 2000 —4000 ' ”2000 Care is required when using a graphing calcuiator to graph a rational function be I cause of the presence of vertical asymptotes. By default, the caicuiator wiil graph in "3 CONNECTED mode.’l‘his can give strange views when vertical asymptotes are pres- if ent.This situation is illustrated in Example 2. 2} Graphing a Rational Function flu ' aPmmmrmmrwa:Irlcvac'nv.9andmm:z‘.maven?its-scurrvw'r'va‘r 'Il’fl'A pal .. .:-‘.- -:- : . 1 . . . , {5 Graph f(x) W x _ z in a standard w1ndow. Change to DOT mode and graph again at the standard window. afielatian l. EnterYi: 1/ (X m l) in ther Editor. Nete that you must enclose the denomina tor X —— 1 in parentheses. Press and then 6 for Erzxtsndard to get the graph in Figure 13.8.4 in...
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