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PART B
TEXAS INSTRUMENTS TI-85/TI-86 GRAPHING
CALCULATORS
Setup
When using this Guide, you should always, unless instructed otherwise, use the calculator setup
specified below for both the TI-85 and TI-86. Before you begin, check the basic setup with
2nd MORE (MODE) . Use the following instructions to choose the settings shown in Figure 1. Check
the window format with GRAPH MORE F3 (FORMT) . Choose the settings shown in Figure 2.
¥ If you do not have the darkened choices shown in Figur
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B-2 TI-85/TI-86 Graphing Calculators , , , ALPHA 7 (L) 2 ALPHA 7 (L) 3 ALPHA 7 (L) 4 ALPHA 7 (L) 5 ENTER . (See Figure 4.) Press EXIT or 2nd EXIT (QUIT) to return to the home screen. TI-85 Statistical Setup TI- 86 Statistical Setup FIGURE 3 FIGURE 4 TI-86 Note: Because appropriate TI-86 computer linking software had not yet been perfected at the time this material was written, TI-86 screens in this Guide appear smaller than the TI- 85 screens. Screens that
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Chapter 1 B-3 - 1 æ ö 1 Calculate using this nice shortcut. ç ÷ 895 ç ÷ 4*15 + è ø 7 (If you wish to clear the home screen, press CLEAR .) 3. ANSWER DISPLAY When the denominator of a fraction has no more than three digits, your calculator can provide the answer in fraction form. When an answer is very large or very small, the calculator displays the result in scientific notation. The Òto a fractionÓ key is obtained by pressing 2nd 5 (MATH) F5 (MISC) MORE F1 ( Frac) . 12 The cal
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B-4 TI-85/TI-86 Graphing Calculators Choose F1 (Goto) to position the cursor to the place the error occurred so that you can correct the mistake or choose F5 (Quit) to begin a new line on the home screen. Copyright © Houghton Mifflin Company. All rights reserved.
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Chapter 1 Ingredients of Change: Functions and Linear Models & 1.1 Fundamentals of Modeling There are many uses for a function that is entered in the graphing list. Graphing the function in an appropriate viewing window is one of these. Because you must enter all functions on one line (that is, you cannot write fractions and exponents the same way you do on paper) it is very important to have a good understanding of the calculatorÕs order of operations and to use parentheses whenever they ar
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B-6 TI-85/TI-86 Graphing Calculators Remove the lower menu with EXIT , and press F3 (ZOOM) MORE F4 (ZDECM) . Notice that the graphics screen is blank. TI-85 Press EXIT F2 (RANGE) to see the view set by ZDECM. TI-86 Press EXIT F2 (WIND) to see the view set by ZDECM. ¥ Both xMin and xMax are the settings of the left and right edges of the viewing screen, and yMin and yMax are the settings for the lower and upper edges of the viewing screen. xScl and yScl set the spacing betwee
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Chapter 1 B-7 Both Press F5 (GRAPH) to draw the graph of y1 = 1000(1 + 0.05^x) in the new view. CLEAR removes the menu from the bottom of the screen if you wish to see more of the graph. Copyright © Houghton Mifflin Company. All rights reserved.
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B-8 TI-85/TI-86 Graphing Calculators 1.1.4 AUTOMATICALLY CHANGING THE VIEW OF THE GRAPH If your view of the graph is not good or if you do not see the graph, change the view using the built-in autoscaling feature of your calculator. This option will automatically find a view to see all the functions that you have turned on in the graphing list. x Be sure the function you are graphing, y = 1000(1 + 0.05) , is entered in the y1 location of the y(x)= list. (Delete all other functions tha
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Chapter 1 B-9 x Estimate the value of A where A = 1000(1 + 0.05) when x = 5, x = 7, and x = 10. Press EXIT F2 (RANGE) (or WINDOW) . If you do not have the settings shown to the right, reset the values. Press F3 (ZOOM) F3 (ZOUT) . After the graph finishes drawing, press ENTER to once more enlarge your view of the graph. (Press EXIT F2 (RANGE) and observe the values Note that (5, 1450) is a point now defining the graphics screen.) on the screen, not a point on the graph of the function
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B-10 TI-85/TI-86 Graphing Calculators Press ENTER to display the output and see the point marked on the graph of the function. Repeat this process to find the outputs when x = 7 and x = 10. To evaluate an output from the home screen: First, press EXIT until you are on the home screen. Store the input value, say 5, in x by with 5 STO x-VAR ENTER . Next, type the location in the y(x)= list in which the function is stored with 2nd ALPHA 0 (y) 1. Note that the second
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Chapter 1 B-11 Evaluate y1 at x = 7 by recalling the previous entry with 2nd ENTER (ENTRY) , edit the 5 to 7 by pressing and typing over the 5, and press ENTER . Repeat the process to evaluate y1 at x = 10. & 1.2 Functions and Graphs When you are asked to estimate or approximate an output or an input value, you can use your calculator in the following ways: ¥ tracing a graph (Sections 1.1.5, 1.1.6) ¥ close values obtained from a table of function values (End of Section 1.2.2) Wh
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B-12 TI-85/TI-86 Graphing Calculators The message that appears tells you to press ENTER to see the output. The output is in the form [ t, v(t) ]. We see that v(85) » $6945. If you had wanted to generate a list of values, starting at a value called TblMin and differing by DTbl, use the AUTO option in the program. Press ENTER to re-run the program, choose 1 for AUTO, and enter the values like those shown to the right. Pressing ENTER and allows you to see the outputs that have been
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Chapter 1 B-13 Press F1 (TABLE) , type in the x-value(s) at which the function is to be evaluated, and press ENTER . You can scroll through the table with , , , and/or . Unwanted input entries can be v(85) » $6945 cleared with DEL . 1.2.2 SOLVING FOR INPUT VALUES Your calculator will solve for input values of an equation that you enter in the SOLVER. You can use any letter you wish for the input variable when using the SOLVER. (Of course, if you are using a function that is entered
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B-14 TI-85/TI-86 Graphing Calculators Notice that you could have typed the v(t), with input variable t, directly in the solver. The solution is, of course, the same. If there is more than one solution to an equation, you need to give the solver an approximate 2 location for each answer. Suppose you are given q(x) = 8x + 54.65x Ð 163 and asked to find what input(s) correspond to an output of q(x) = 154. (The procedure outlined below also applies to finding where two functions are eq
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Chapter 1 B-15 Press F4 (TRACE) and use and/or to move along the graph of the equation in y1. Press to jump from the graph of y1 to the graph of y2. Tracing reveals that guesses for the input values – where these two graph intersect are x » 10.6, x »3.8. Return to the home screen with 2nd EXIT (QUIT) . Access the SOLVER and enter the equation y1 = y2 as shown on the right. Enter the guess for the left- most intersection point and solve for x. Enter the guess for the rightmost inte
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B-16 TI-85/TI-86 Graphing Calculators To graphically find an x-intercept, i.e., a value of x at which the graph crosses the horizontal axis, first press EXIT to return the menu to the bottom of the screen. TI-85 Press F1 (MATH) F3 (ROOT ) TI-86 Press F1 (MATH) F1 (ROOT ) Both Use to move the trace cursor near the first x-intercept, and press ENTER . To find the second x-intercept, press EXIT and the F-key under ROOT, use to move the trace cursor near the other x-intercep
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Chapter 1 B-17 On the TI-85, ¥ The TI-85 interprets y1(y2) as the product of y1 and y2. To have the calculator graph the composite function f(g(x)), you should substitute g(x) everywhere an x appears in f(x). 2 2 For instance, if f(x) = x - 1 is in y1 and g(x) = 0.3x + 5 is in y2, enter y7 = y2 Ð 1 for the o composite function (f g)(x) . On the TI-86, o ¥ Enter y1(y2 ) in y7 to obtain the composite function (f g)(x) = f(g(x)). Both Your calculator will evaluate and graph thes
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B-18 TI-85/TI-86 Graphing Calculators Because the two pieces are close together at x = 90, you may need to take a closer look to see the break. However, because the calculator draws graphs by connecting function outputs wherever the function is defined, it will connect the two pieces unless you tell it not to do so by pressing MORE F5 (FORMT) , use and to choose DrawDot. Press ENTER . Now, take a closer look with F5 (GRAPH) and F3 ZOOM F2 (ZIN ) . To keep the point where the func
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Chapter 1 B-19 After setting the proper horizontal view, you can now use ZFIT to draw a graph of the piecewise function. You can find function values by evaluating outputs on the home screen or using the table. & 1.4 Linear Functions and Models Actual real-world data is used throughout Calculus Concepts. It is necessary that you use your calculator to find a curve that models the data. Be very careful when you enter the data in your calculator because your model and all of your result
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B-20 TI-85/TI-86 Graphing Calculators To enter data using the list editor, Press 2nd – (LIST) F4 (EDIT) to access the list editor. Enter the name L2 at the name prompt and press ENTER . If there are data values in this list, see 1.4.3 of this Guide and Enter the first y-value as e1, press ENTER or , first delete the ÒoldÓ data. enter the second y-value as e2, etc. TI-86 Even though both of the methods discussed above are ways to enter data on the TI-86, the most convenient method
