Shading on the TI-86

Chapter 2, Section 1 of the Pre-Calculus text contains graphs Example 14 and for Example 15. Those graphs, or ones quite similar to them, are re-produced here.

Example 14: Graph y (3/4)x -3	Example 15: Graph y₁ = 5x + 2 and y₂ = x – 6 and shade the region where y₁ y₂

This page demonstrates the steps needed to produce these graphs on the TI-86.

Figure 1 We start by moving to the graph menu via the key and then selecting the y(x)= option via the key. This produces Figure 1.
Figure 2 In Figure 2 we have entered the line we wish to graph via the keys and . Note that this is an equality. We expect that the graph will be a line.

Figure 3 We leave Figure 2 and move to Figure 3 by pressing and . The resulting graph, done with the Zoom Standard settings, is the expected line. However, we wanted to prduce the graph in the book. It has "shaded" the portion of the graph above the line.

Figure 4 We return to the y(x)= screen via the key. Note that the resulting sub-menu has options not currently displayed. This is indicated by the small arrow at the extreme right of the menu.

Figure 5 We press to see the additional options. These are shown in Figure 5. The third option, STYLE, is the one that we will be using. That option allows us to change the style for the graph.

Figure 6 Figure 6 is the result of pressing . The only visible change from Figure 5 to FIgure 6 is the alteration of the "style indicator", the small icon to the left of our function definition. In Figure 6 that icon suggests shading above the graph of the function.

Figure 7 We return to redraw the graph by pressing to select the GRAPH option from the upper menu of Figure 6. This Figure does indeed look like the one inthe textbook, except that we have the menu displayed in Figure 7.

Figure 8 We can hide that menu, from Figure 7, by pressing the key. The result is Figure 8.

We have produced the graph for Example 14 from the textbook. Example 15 requires us to shade an area between two functions. We do not do this with the normal graphing commands. Rather, the TI-85 and TI-86 have a special command called Shade to do this task. In preparation for using the Shade command we will clear off the graph generated above.

Figure 9 In Figure 8 we had hidden the menu. We press to resore that menu. Then we press to select the y(x)= option and to return us to the screen shown in Figure 9.

Figure 10 Pressing the key will remove our sngle function definition.

Figure 11 Our next goal will be to start the Shade command. We can find that command on a sub-menu under the Graph menu. However, we want to get out of the y(x)= screen. Therefore, we press to close the sub-menu, and then to close the main menu. That way we can press to re-open the Graph menu, but to do so outside of the y(x)= screen. Finally, we generate Figure 11 by pressing the key to see additional menu options.

Figure 12 We select the DRAW option by pressing the key. This will open the sub-menu shown in Figure 12. We note that Shade is the first option in that sub-menu.

Figure 13 We press to select the Shade command. The calculator responds by pasting Shade( onto the screen.

Figure 14 We complete the basic form of the Shade command by giving the expression for the lower function (pressing ), then generating a comma via , then giving the expression for the upper function (pressing , and ending the command with a closing right parenthesis, . The command indicates that the calculator should DRAW the two functions and it should fill in any part of the screen that is above the "lower" function and below the "upper" function.

Figure 15 We constructed the Shade command in Figure 14. Now, press to perform the command. The calculator responds with Figure 15. Actually, as the calculator draws the graph, it is clear that the desired shading has been done. However, once the menu of Figure 15 has been displayed, we can no longer see the shaded portion of the graph.

Figure 16 As before, we can press to hide the menu and produce Figure 16.
Still, this is not quite the display that we want to produce. We need to change the WINDOW settings so that we can squeeze more of the range values onto the screen.

Figure 17 We press to restore the menu, and then to open the WINDOW screen. As expected, the settings shown in Figure 17 are those of the Zoom Standard feature.

Figure 18 We will aler those settings by changing the minimum y value. We press to move the highlight down to the yMin line. Then we press to enter the new value.

Figure 19 We return to the graphics screen by pressing the key. This has been done to generate Figure 19. But our shaded gaph has disappeared. It has gone away because we changed the WINDOW settigs and because it was DRAWn, not graphed, by the Shade command.

Figure 20 We leave the graphics display of Figure 19 by pressing the key. This returns us to the normal screen we we see the Shade command as our last command.

Figure 21 We need only press to execute that lst command again and therefore to draw the lines and shaded region shown in Figure 21. This is more similar to the graph in the textbook. We need only hide the menu to have our image be almost identical to that graph.

Figure 1	We start by moving to the graph menu via the key and then selecting the y(x)= option via the key. This produces Figure 1.
Figure 2	In Figure 2 we have entered the line we wish to graph via the keys and . Note that this is an equality. We expect that the graph will be a line.
Figure 3	We leave Figure 2 and move to Figure 3 by pressing and . The resulting graph, done with the Zoom Standard settings, is the expected line. However, we wanted to prduce the graph in the book. It has "shaded" the portion of the graph above the line.
Figure 4	We return to the y(x)= screen via the key. Note that the resulting sub-menu has options not currently displayed. This is indicated by the small arrow at the extreme right of the menu.
Figure 5	We press to see the additional options. These are shown in Figure 5. The third option, STYLE, is the one that we will be using. That option allows us to change the style for the graph.
Figure 6	Figure 6 is the result of pressing . The only visible change from Figure 5 to FIgure 6 is the alteration of the "style indicator", the small icon to the left of our function definition. In Figure 6 that icon suggests shading above the graph of the function.
Figure 7	We return to redraw the graph by pressing to select the GRAPH option from the upper menu of Figure 6. This Figure does indeed look like the one inthe textbook, except that we have the menu displayed in Figure 7.
Figure 8	We can hide that menu, from Figure 7, by pressing the key. The result is Figure 8.

Figure 9	In Figure 8 we had hidden the menu. We press to resore that menu. Then we press to select the y(x)= option and to return us to the screen shown in Figure 9.
Figure 10	Pressing the key will remove our sngle function definition.
Figure 11	Our next goal will be to start the Shade command. We can find that command on a sub-menu under the Graph menu. However, we want to get out of the y(x)= screen. Therefore, we press to close the sub-menu, and then to close the main menu. That way we can press to re-open the Graph menu, but to do so outside of the y(x)= screen. Finally, we generate Figure 11 by pressing the key to see additional menu options.
Figure 12	We select the DRAW option by pressing the key. This will open the sub-menu shown in Figure 12. We note that Shade is the first option in that sub-menu.
Figure 13	We press to select the Shade command. The calculator responds by pasting Shade( onto the screen.
Figure 14	We complete the basic form of the Shade command by giving the expression for the lower function (pressing ), then generating a comma via , then giving the expression for the upper function (pressing , and ending the command with a closing right parenthesis, . The command indicates that the calculator should DRAW the two functions and it should fill in any part of the screen that is above the "lower" function and below the "upper" function.
Figure 15	We constructed the Shade command in Figure 14. Now, press to perform the command. The calculator responds with Figure 15. Actually, as the calculator draws the graph, it is clear that the desired shading has been done. However, once the menu of Figure 15 has been displayed, we can no longer see the shaded portion of the graph.
Figure 16	As before, we can press to hide the menu and produce Figure 16. Still, this is not quite the display that we want to produce. We need to change the WINDOW settings so that we can squeeze more of the range values onto the screen.
Figure 17	We press to restore the menu, and then to open the WINDOW screen. As expected, the settings shown in Figure 17 are those of the Zoom Standard feature.
Figure 18	We will aler those settings by changing the minimum y value. We press to move the highlight down to the yMin line. Then we press to enter the new value.
Figure 19	We return to the graphics screen by pressing the key. This has been done to generate Figure 19. But our shaded gaph has disappeared. It has gone away because we changed the WINDOW settigs and because it was DRAWn, not graphed, by the Shade command.
Figure 20	We leave the graphics display of Figure 19 by pressing the key. This returns us to the normal screen we we see the Shade command as our last command.
Figure 21	We need only press to execute that lst command again and therefore to draw the lines and shaded region shown in Figure 21. This is more similar to the graph in the textbook. We need only hide the menu to have our image be almost identical to that graph.