Chapter 1 Section 0 Example 4 on the TI-86

Note that the TI-86 and the TI-85 have slightly different keys. This page uses the keys associated with the TI-86. The differences are in the "2^nd" functions on some of the keys used here. The TI-85 keys will have the same key-face symbol unless otherwise noted.

Example 4 in the textbook contains a TI-86 solution. The problem is to evaluate

11x⁵ + 12x⁴ - 10x³ +6x² + 15 for x=1.5 The solution given uses the evalF function on the calculator. This is a good solution, and we will step through doing it below. In addition, we will look at the more general solution of assigning a value to the variable x and then entering the expression.

Figure 1 In order to use evalF we need to find it. It appears in the CALC menu. To open that menu we can press the keys. Figure 1 shows that menu at the bottom. We note that evalF is in the first position of the menu. Thus, we press to paste evalF onto the screen, as shown in Figure 2.
Figure 2 Notice that the left parenthesis is appended to evalF on the screen. We will need to complete the function statement. evalF has three "arguments", values that are given to the function. The first is the expression to evaluate. For us, this is 11x⁵ + 12x⁴ - 10x³ +6x² + 15 Between the first argument and the second we place a comma. The second argument is the variable in the expression that is to be replaced by a value. For us, this is the variable x. There is a comma between the second and third argument. The final argument is the value that is to be used in place of the variable. For us that value is 1.5.

Figure 3 Figure 3 has the complete statement of the function with all three arguments given, with a comma between arguments, and with a closing right parenthesis. The comma can be found on the key.
NOTE: The example given here is using the lower case letter x for the variable. Remember that the TI-86 (and the TI-85) are case sensitive. They distinguish between a variable x and a different one X. The lower case x is used so often that there a special key that produces it without requiring the use of the ALPHA key. In particular, the function in Figure 3 was produced using the key. A strange side-effect of using the key is that the calculator puts an extra space before the variable as it is pasted onto the screen. A close look at Figure 3 will confirm the presence of those extra spaces.

Figure 4 Pressing the key will cause the machine to execute the function, that is, to evaluate the expression given as the first argument, with the variable that is the second argument replaced by the value that is given as the third argument. The result is 139.03135, but this is a decimal answer and we would like to have it expressed as a fraction. Therefore, in Figure 4, we have recalled the previous command by pressing the keys. Then we will move to the CUSTOM menu so that we can select the operation.

Figure 5 To get to Figure 5 we have pressed the key to open the CUSTOM menu. Then we pressed the key to paste onto our command. Finally, we pressed to perform the function and to convert the answer to a fraction. The result is 4449/32.

Figure 6 Figure 6 demonstates a different approach to doing the problem. Here we assign the value 1.5 to the variable x. Then, we merely type the expression that we want evaluated. Again, we are using the lower case x, and the key to produce it on the screen. Note that the answer is the same as we found in Figure 5.

Figure 7 To try to convert that answer to a fraction we can simply press the key which will paste onto the screen, but, because we are at the start of a new command, the calculator will supply the Ans before pasting the . Then, we press to perform the command and we again find the answer to be 4449/32.

Figure 1	In order to use evalF we need to find it. It appears in the CALC menu. To open that menu we can press the keys. Figure 1 shows that menu at the bottom. We note that evalF is in the first position of the menu. Thus, we press to paste evalF onto the screen, as shown in Figure 2.
Figure 2	Notice that the left parenthesis is appended to evalF on the screen. We will need to complete the function statement. evalF has three "arguments", values that are given to the function. The first is the expression to evaluate. For us, this is 11x⁵ + 12x⁴ - 10x³ +6x² + 15 Between the first argument and the second we place a comma. The second argument is the variable in the expression that is to be replaced by a value. For us, this is the variable x. There is a comma between the second and third argument. The final argument is the value that is to be used in place of the variable. For us that value is 1.5.
Figure 3	Figure 3 has the complete statement of the function with all three arguments given, with a comma between arguments, and with a closing right parenthesis. The comma can be found on the key. NOTE: The example given here is using the lower case letter x for the variable. Remember that the TI-86 (and the TI-85) are case sensitive. They distinguish between a variable x and a different one X. The lower case x is used so often that there a special key that produces it without requiring the use of the ALPHA key. In particular, the function in Figure 3 was produced using the key. A strange side-effect of using the key is that the calculator puts an extra space before the variable as it is pasted onto the screen. A close look at Figure 3 will confirm the presence of those extra spaces.
Figure 4	Pressing the key will cause the machine to execute the function, that is, to evaluate the expression given as the first argument, with the variable that is the second argument replaced by the value that is given as the third argument. The result is 139.03135, but this is a decimal answer and we would like to have it expressed as a fraction. Therefore, in Figure 4, we have recalled the previous command by pressing the keys. Then we will move to the CUSTOM menu so that we can select the operation.
Figure 5	To get to Figure 5 we have pressed the key to open the CUSTOM menu. Then we pressed the key to paste onto our command. Finally, we pressed to perform the function and to convert the answer to a fraction. The result is 4449/32.
Figure 6	Figure 6 demonstates a different approach to doing the problem. Here we assign the value 1.5 to the variable x. Then, we merely type the expression that we want evaluated. Again, we are using the lower case x, and the key to produce it on the screen. Note that the answer is the same as we found in Figure 5.
Figure 7	To try to convert that answer to a fraction we can simply press the key which will paste onto the screen, but, because we are at the start of a new command, the calculator will supply the Ans before pasting the . Then, we press to perform the command and we again find the answer to be 4449/32.