Chapter 1, Section 2, Example 15 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.

The following screen images trace the steps needed to generate a graph on a TI-86 for the solution to the problem given as

3(x + 2) - 5x 4x This solution uses the relational operation

and the fact that the TI-86 respresents the value TRUE by the number 1 and it represents the value FALSE by the number 0.

Figure 1 We have opened the GRAPH menu in Figure 1 by pressing the key. The calculator used to generate these screens did not have any previously defined graphs on it. Therefore, the screen shown here is blank except for the menu at the bottom. Had a graph been defined earlier on the calculator, that graph would have been displayed, along with the menu. In any case, it is only the menu that we are interested in at this point.

Figure 2 We can press the key to leave Figure 1 and move to Figure 2. Again, the screen shown here is empty because no graph had been defined earlier. Had a graph been defined earlier the function definition would have appeared here. In that case we could use the CLEAR key to remove to old definition (or definitions), and to change the screen so that it appears as in Figure 2.
Figure 2, as shgwn, indicates that the calculator is ready for us to enter our new function.

Figure 3 For Figure 3 we have started to enter the problem. We have done this via the keys . Now we need to generate the "less than or equal to" sign, . It is not on the keyboard.

Figure 4 To find the we need to open a new menu, the TEST menu. To do this we press the keys. The result is Figure 4. The TEST sub-menu has the character that we want to use.

Figure 5 For Figure 5 we can complete the definition by pressing to select the from the menu, followed by .

Figure 6 In order to close the sub-menu, we press . This changes the display to that shown in Figure 6.

Figure 7 Then, to open the ZOOM menu, we can press the keys to select the middle option inthe upper menu. Figure 7 illustrates the ZOOM sub-menu. We can press to choose the ZSTD option from the menu.

Figure 8 The resulting graph is shown in Figure 8. The solution to the original problem, 3(x + 2) - 5x 4x is the set of values where the graph is raised, in this case, values of x greater than or equal to 1. That is, for any value of x that makes the expression true, the resulting graph will have the value 1. For values of x that make the inequality false, the graph is at level 0, which, unfortunately, means that the graph is right on top of the x-axis.
Evaluating
3(x + 2)x - 5x 4x produces either a 0 (for FALSE) or a 1 (for TRUE). If we multiply the expression by 3 and then subtract 1, then evaluating the new inequality (3(x + 2)x - 5 4x)*3–1 will result in a ^–1 for FALSE and a 2 for TRUE.

Figure 9 We will make the changes to the function and then graph the new version. First, we return to the y= screen by pressing . This brings up the screen shown in Figure 9. Note that the blinking cursor has been caught covering up the "3" at the start of the expression. We want to insert a left parenthesis before the "3". We can shift the calculator into "insert" mode by pressing the keys. The result is shown in Figure 10.

Figure 10 The blinking block cursor of Figure 9 has been changed to a blinking underscore cursor in Figure 10. This indicates that we are in "insert" mode.

Figure 11 For Figure 11 we have pressed the key. The calculator has inserted the left parenthesis before the bkinking underscore cursor.

Figure 12 To complete the change we want to move to the right end of the expression and add ")*3–1". We can do this by pressing to move the the right end, and then to complete the task.
To leave this figure and move to Figure 13, press to choose the GRAPH option in the top menu.

Figure 13 We can now see the portion of the graph that is negative, representing values of x where the inequality is false, and the portion of the gaph that is positive, representing values of x where the inequality is true.

Figure 1	We have opened the GRAPH menu in Figure 1 by pressing the key. The calculator used to generate these screens did not have any previously defined graphs on it. Therefore, the screen shown here is blank except for the menu at the bottom. Had a graph been defined earlier on the calculator, that graph would have been displayed, along with the menu. In any case, it is only the menu that we are interested in at this point.
Figure 2	We can press the key to leave Figure 1 and move to Figure 2. Again, the screen shown here is empty because no graph had been defined earlier. Had a graph been defined earlier the function definition would have appeared here. In that case we could use the CLEAR key to remove to old definition (or definitions), and to change the screen so that it appears as in Figure 2. Figure 2, as shgwn, indicates that the calculator is ready for us to enter our new function.
Figure 3	For Figure 3 we have started to enter the problem. We have done this via the keys . Now we need to generate the "less than or equal to" sign, . It is not on the keyboard.
Figure 4	To find the we need to open a new menu, the TEST menu. To do this we press the keys. The result is Figure 4. The TEST sub-menu has the character that we want to use.
Figure 5	For Figure 5 we can complete the definition by pressing to select the from the menu, followed by .
Figure 6	In order to close the sub-menu, we press . This changes the display to that shown in Figure 6.
Figure 7	Then, to open the ZOOM menu, we can press the keys to select the middle option inthe upper menu. Figure 7 illustrates the ZOOM sub-menu. We can press to choose the ZSTD option from the menu.
Figure 8	The resulting graph is shown in Figure 8. The solution to the original problem, 3(x + 2) - 5x 4x is the set of values where the graph is raised, in this case, values of x greater than or equal to 1. That is, for any value of x that makes the expression true, the resulting graph will have the value 1. For values of x that make the inequality false, the graph is at level 0, which, unfortunately, means that the graph is right on top of the x-axis. Evaluating 3(x + 2)x - 5x 4x produces either a 0 (for FALSE) or a 1 (for TRUE). If we multiply the expression by 3 and then subtract 1, then evaluating the new inequality *(3(x + 2)x - 5 4x)3–1 will result in a ^–1 for FALSE and a 2 for TRUE**.
Figure 9	We will make the changes to the function and then graph the new version. First, we return to the y= screen by pressing . This brings up the screen shown in Figure 9. Note that the blinking cursor has been caught covering up the "3" at the start of the expression. We want to insert a left parenthesis before the "3". We can shift the calculator into "insert" mode by pressing the keys. The result is shown in Figure 10.
Figure 10	The blinking block cursor of Figure 9 has been changed to a blinking underscore cursor in Figure 10. This indicates that we are in "insert" mode.
Figure 11	For Figure 11 we have pressed the key. The calculator has inserted the left parenthesis before the bkinking underscore cursor.
Figure 12	To complete the change we want to move to the right end of the expression and add "*)3–1". We can do this by pressing to move the the right end, and then to complete the task. To leave this figure and move to Figure 13, press to choose the GRAPH** option in the top menu.
Figure 13	We can now see the portion of the graph that is negative, representing values of x where the inequality is false, and the portion of the gaph that is positive, representing values of x where the inequality is true.