Introduction to Tables on the TI-89

The TABLE feature of the TI-89 calculator allows us to view multiple evaluations of different expressions on one screen. For example, if we have two functions, f(x)=2x+1 and g(x)=x²-4, we might be interested in the values of f(x) and g(x) for each of the x values in the set {-3, -2.5, -2, -1.5, -1, -0.5, 0}. The TABLE feature of the TI-89 will allow us to do this, and more.

This set of screen starts with an examination of the TABLE SETUP window. We want to look at this window first because it determines just how the TABLE screen works.

Figure 1 Figure 1 shows a blank HOME screen. If need be, you can press the key to move to this screen.
Figure 2 We press the keys to open the TblSet window. The result is shown in Figure 2, although the highlighted area and values may be different on a different calculators. Note that the calculator used to generate Figure 2 had the value 0 under the blinking cursor.
The challenge from the openning paragraph was to look at the set of values
{-3, -2.5, -2, -1.5, -1, -0.5, 0}. To do this we want the value to be set at -3. This will be the initial value in our table.

Figure 3 We enter the desired value, ^–3, into the area by pressing . Then we press to accept our value,and to move the highlight to the next area. This leaves the screen as is shown in Figure 3.

Figure 4 With set to -3, the next thing that we want to do is to set the change from one value to the next. In our case, we want the values to increase by 0.5. We left Figure 3 with the highlight already on the field. We set this field to be .5 by pressing the and keys. Then we can move the highlight down two fields by pressing . This is the state shown in Figure 4.

Figure 5 The TABLE SETUP window shown in Figure 4 had the Independent: value set at AUTO, and we had moved the highlight to that field. The Independent: field controls how the calculator deals with the independent variable. In our example, that is the x variable. This is the variable that will take on the values that we select. The calculator will either determine these values AUTOmatically, or it will ASK us for them. We can see these acceptable values by pressing the key. This brings up the selection list shown in Figure 5. We want to use the and settings to automatically generate independent values. Therefore, we really do want to have the AUTO setting.

Figure 6 We can reselect B from Figure 5 by pressing . Then we can accept and save all of the new values on the window by pressing the key. This will return us to the HOME screen shown in Figure 6.

Figure 7 Now it is time for us to enter the functions that we want to use in our table. To do this we will want to move to the y= screen. We press to change to the y= screen.

Figure 8 We had two functions to evaluate, y = 2x + 1
y = x² – 4 Figure 8 shows the result of pressing to generate the first function, to accept that first function and to get the calculator ready to accept the second, and then to form the second function in the input area at the bottom of the screen.

Figure 9 All that remains is to press to accept that second function. Doing so leaves the calculator as shown in Figure 9.

Figure 10 After adjusting up the TABLE SETUP screen earlier, and now defining the functions in Figure 9, we are ready to look at the table. To do so we press . In the first column, the calculator displays values for the independent variable, x, starting with our value, ^–3, and increasing by our value, 0.5. The second column shows the corresponding values for the first function, while the third column shows the corresponding values for the second function.

Figure 11 We can move down the table by pressing to move the highlight as shown in Figure 11. It would appear, in Figure 11, that the calculator has stopped the table after the highlighted entry. There is a blank row beneath the highlighted row. In fact, the calculator is merely waiting for us to move the highlight down one row, at which point the calculator will compute new values for each of the three columns.

Figure 12 In Figure 12 we have pressed to move the cursor down three rows, thus generating three new sets of values. Note that we seem to have lost the old top rows. Figure 12 now has the value ^–1.5 as its top value for x.

Figure 13 As we might expect, we could press 14 times to move the highlight to new values at the top of the screen. Figure 13 reflects such a move, forcing the top x value to be ^–6.5 with appropriate new values in the second and third columns.

Figure 14 Of course, we could press to return to the y= screen to allow us to define a new function. We have done just that to generate Figure 14.

Figure 15 Note that the highlight in Figure 14 was in the upper portion of the screen, next to the y3= definition. By pressing the key, we direct the calculator to move to the input line so that we can specify a new function. This is shown in Figure 15.

Figure 16 Our new funtion will be y3=(x+2)(x–1) We enter that function by pressing and .

Figure 17 To accept the funtion we press . The result is shown in Figure 17.

Figure 18 When we return to the TABLE screen via the keys, the new functional values are displayed in the rightmost column.

Figure 19 The starting value for our independent variable, x, in Figure 18 was ^–6.5, exactly as we had left it in Figure 13. In Figure 19 we use the keys to return to the TABLE SETUP window, where we can inspect the current values. Note that the value is now ^–6.5, which reflects the current TABLE screen values. As we scroll through the TABLE the calculator adjusts the value associated with appropriately.

Figure 20 Now that we are on the TABLE SETUP window, we can modify the values before we return to the TABLE screen. In Figure 20 we have pressed to move the highlight to the setting, and then we have pressed to generate a new value.

Figure 21 We press to accept that value, and to save the current settings. This will cause us to return to the TABLE screen shown in Figure 21. Note that the steps for the independent variable, x, have been modified as we specified, and that new values for the three defined functions are displayed.

Figure 22 One of the limittions of the TABLE screen is that the values in the table are rounded to fit the available space. For example, we press and to move the cursor to the second row of values in the rightmost column, shown in Figure 22. In that "cell" the value 30.813 is highlighted. However, at the bottom of the screen, in the input line, the more precise value, namely 30.8125 is shown.
Also, note in Figure 22, that the tabs at the top of the screen indicate that the F4 key will perform the HEADER operation.

Figure 23 If we press in Figure 22, the calculator responds with Figure 23, where the function definition for the column holding the highlighted cell, has been placed into the input line at the bottom of the screen.

Figure 24 We will change the function by editing it at this point. We press to move the cursor to the right end of the definition. Then press to move the cursor between the 1 and the ). Next, press to remove the 1. And, finally, press to complete the change to (x+2)(x–3)

Figure 25 Press to accept the new definition from the input line of Figure 24 and return the screen to the TABLE, shown in Figure 25. Note the new values in the rightmost column reflecting the change in the function definition.

Figure 26 In fact, if we return to the y= scrren via the keys, we can see, in Figure 26, that the actual definition of y3 has been altered.

Up to this point we have used the AUTOmatic features of the TABLE system to create and change the values of the independent variable, x. Now we will use a few Figures to demonstrate the ASK feature. Once Independent: has been set to ASK, the calculator will allow us to enter values for the independent variable, rather than use the and settings.

Figure 27 We will need to return to the TABLE SETUP window. We do this by pressing the and keys. Then we can move the highlight down to the Independent: setting by using the keys.

Figure 28 We want to change the value of the Independent: setting. We press to see the options, and then to highlight our desired choice, ASK.

Figure 29 Press to make the highlighted choice of Figure 28 the actual setting, as shown in Figure 29. Notice in Figure 29 that the old values for and remain as a reminder, but that they are no longer available to us. This is an indication that those values will not be used as far as maintaining the actual TABLE.

Figure 30 We can press to save the values set in Figure 29, and then press to return to the TABLE screen, shown in Figure 30. We note that although the TABLE values have not changed from the TABLE that we saw in Figure 25, the "tab" choices at the top of the screen have changed. We now have six options associated with our F1-F6 keys.

Figure 31 The current TABLE is operating under the ASK setting. Therefore, we can change the values of the independent variable, x. We do this by highlighting an x value, as we had in Figure 30, and then pressing the key. Note that the highlight in Figure 31 has moved to the input line at the bottom of the screen.

Figure 32 We can change the value of the independent variable, x, by entering a new value at this point. We press to enter the value 2.145.

Figure 33 We press to accept this new value and to place it into the table. Note, in Figure 33, that our value 2.145 has been inserted into the TABLE, and that new values have been created for the three functions defined for the next three columns.

Figure 34 To arrive at Figure 34 we press to move the highlight to the next row, to shift the highlight to the input line, and to enter the value 3.

Figure 35 As before, we press to accept that new value, place it into the TABLE, and cause new values to be computed for the other columns.

Figure 36 Let us move to the last value in the table, ^–5.5, and change it to 3.01. We press to shift the highlight, to move to the input line, and to enter our new value.

Figure 37 Pressing will complete the task started in Figure 36. Now we will move to the open line at the bottom of the TABLE. We do this by pressing . We want to enter a new value in this spot. Therefore, we press to move the highlight to the input line, and then to enter our new value. This is reflected in Figure 37.

Figure 38 In Figure 37 we had specified the new value, but we had not accepted it. We press to accept that new value, as shown in Figure 38.

Figure 39 For Figure 39, we move down to the open line via the key. Then we use the key to move to the input line. We enter a new value, 3.0125, by pressing . We accept that value by pressing , and then we shift over two columns by using the key sequence. Note, again, that although the TABLE display gives a truncated version of the value, we can see the full approximation of the highlighted value in the input line.

Figure 1	Figure 1 shows a blank HOME screen. If need be, you can press the key to move to this screen.
Figure 2	We press the keys to open the TblSet window. The result is shown in Figure 2, although the highlighted area and values may be different on a different calculators. Note that the calculator used to generate Figure 2 had the value 0 under the blinking cursor. The challenge from the openning paragraph was to look at the set of values {-3, -2.5, -2, -1.5, -1, -0.5, 0}. To do this we want the value to be set at -3. This will be the initial value in our table.
Figure 3	We enter the desired value, ^–3, into the area by pressing . Then we press to accept our value,and to move the highlight to the next area. This leaves the screen as is shown in Figure 3.
Figure 4	With set to -3, the next thing that we want to do is to set the change from one value to the next. In our case, we want the values to increase by 0.5. We left Figure 3 with the highlight already on the field. We set this field to be .5 by pressing the and keys. Then we can move the highlight down two fields by pressing . This is the state shown in Figure 4.
Figure 5	The TABLE SETUP window shown in Figure 4 had the Independent: value set at AUTO, and we had moved the highlight to that field. The Independent: field controls how the calculator deals with the independent variable. In our example, that is the x variable. This is the variable that will take on the values that we select. The calculator will either determine these values AUTOmatically, or it will ASK us for them. We can see these acceptable values by pressing the key. This brings up the selection list shown in Figure 5. We want to use the and settings to automatically generate independent values. Therefore, we really do want to have the AUTO setting.
Figure 6	We can reselect B from Figure 5 by pressing . Then we can accept and save all of the new values on the window by pressing the key. This will return us to the HOME screen shown in Figure 6.
Figure 7	Now it is time for us to enter the functions that we want to use in our table. To do this we will want to move to the y= screen. We press to change to the y= screen.
Figure 8	We had two functions to evaluate, y = 2x + 1 y = x² – 4 Figure 8 shows the result of pressing to generate the first function, to accept that first function and to get the calculator ready to accept the second, and then to form the second function in the input area at the bottom of the screen.
Figure 9	All that remains is to press to accept that second function. Doing so leaves the calculator as shown in Figure 9.
Figure 10	After adjusting up the TABLE SETUP screen earlier, and now defining the functions in Figure 9, we are ready to look at the table. To do so we press . In the first column, the calculator displays values for the independent variable, x, starting with our value, ^–3, and increasing by our value, 0.5. The second column shows the corresponding values for the first function, while the third column shows the corresponding values for the second function.
Figure 11	We can move down the table by pressing to move the highlight as shown in Figure 11. It would appear, in Figure 11, that the calculator has stopped the table after the highlighted entry. There is a blank row beneath the highlighted row. In fact, the calculator is merely waiting for us to move the highlight down one row, at which point the calculator will compute new values for each of the three columns.
Figure 12	In Figure 12 we have pressed to move the cursor down three rows, thus generating three new sets of values. Note that we seem to have lost the old top rows. Figure 12 now has the value ^–1.5 as its top value for x.
Figure 13	As we might expect, we could press 14 times to move the highlight to new values at the top of the screen. Figure 13 reflects such a move, forcing the top x value to be ^–6.5 with appropriate new values in the second and third columns.
Figure 14	Of course, we could press to return to the y= screen to allow us to define a new function. We have done just that to generate Figure 14.
Figure 15	Note that the highlight in Figure 14 was in the upper portion of the screen, next to the y3= definition. By pressing the key, we direct the calculator to move to the input line so that we can specify a new function. This is shown in Figure 15.
Figure 16	Our new funtion will be y3=(x+2)(x–1) We enter that function by pressing and .
Figure 17	To accept the funtion we press . The result is shown in Figure 17.
Figure 18	When we return to the TABLE screen via the keys, the new functional values are displayed in the rightmost column.
Figure 19	The starting value for our independent variable, x, in Figure 18 was ^–6.5, exactly as we had left it in Figure 13. In Figure 19 we use the keys to return to the TABLE SETUP window, where we can inspect the current values. Note that the value is now ^–6.5, which reflects the current TABLE screen values. As we scroll through the TABLE the calculator adjusts the value associated with appropriately.
Figure 20	Now that we are on the TABLE SETUP window, we can modify the values before we return to the TABLE screen. In Figure 20 we have pressed to move the highlight to the setting, and then we have pressed to generate a new value.
Figure 21	We press to accept that value, and to save the current settings. This will cause us to return to the TABLE screen shown in Figure 21. Note that the steps for the independent variable, x, have been modified as we specified, and that new values for the three defined functions are displayed.
Figure 22	One of the limittions of the TABLE screen is that the values in the table are rounded to fit the available space. For example, we press and to move the cursor to the second row of values in the rightmost column, shown in Figure 22. In that "cell" the value 30.813 is highlighted. However, at the bottom of the screen, in the input line, the more precise value, namely 30.8125 is shown. Also, note in Figure 22, that the tabs at the top of the screen indicate that the F4 key will perform the HEADER operation.
Figure 23	If we press in Figure 22, the calculator responds with Figure 23, where the function definition for the column holding the highlighted cell, has been placed into the input line at the bottom of the screen.
Figure 24	We will change the function by editing it at this point. We press to move the cursor to the right end of the definition. Then press to move the cursor between the 1 and the ). Next, press to remove the 1. And, finally, press to complete the change to (x+2)(x–3)
Figure 25	Press to accept the new definition from the input line of Figure 24 and return the screen to the TABLE, shown in Figure 25. Note the new values in the rightmost column reflecting the change in the function definition.
Figure 26	In fact, if we return to the y= scrren via the keys, we can see, in Figure 26, that the actual definition of y3 has been altered.

Figure 27	We will need to return to the TABLE SETUP window. We do this by pressing the and keys. Then we can move the highlight down to the Independent: setting by using the keys.
Figure 28	We want to change the value of the Independent: setting. We press to see the options, and then to highlight our desired choice, ASK.
Figure 29	Press to make the highlighted choice of Figure 28 the actual setting, as shown in Figure 29. Notice in Figure 29 that the old values for and remain as a reminder, but that they are no longer available to us. This is an indication that those values will not be used as far as maintaining the actual TABLE.
Figure 30	We can press to save the values set in Figure 29, and then press to return to the TABLE screen, shown in Figure 30. We note that although the TABLE values have not changed from the TABLE that we saw in Figure 25, the "tab" choices at the top of the screen have changed. We now have six options associated with our F1-F6 keys.
Figure 31	The current TABLE is operating under the ASK setting. Therefore, we can change the values of the independent variable, x. We do this by highlighting an x value, as we had in Figure 30, and then pressing the key. Note that the highlight in Figure 31 has moved to the input line at the bottom of the screen.
Figure 32	We can change the value of the independent variable, x, by entering a new value at this point. We press to enter the value 2.145.
Figure 33	We press to accept this new value and to place it into the table. Note, in Figure 33, that our value 2.145 has been inserted into the TABLE, and that new values have been created for the three functions defined for the next three columns.
Figure 34	To arrive at Figure 34 we press to move the highlight to the next row, to shift the highlight to the input line, and to enter the value 3.
Figure 35	As before, we press to accept that new value, place it into the TABLE, and cause new values to be computed for the other columns.
Figure 36	Let us move to the last value in the table, ^–5.5, and change it to 3.01. We press to shift the highlight, to move to the input line, and to enter our new value.
Figure 37	Pressing will complete the task started in Figure 36. Now we will move to the open line at the bottom of the TABLE. We do this by pressing . We want to enter a new value in this spot. Therefore, we press to move the highlight to the input line, and then to enter our new value. This is reflected in Figure 37.
Figure 38	In Figure 37 we had specified the new value, but we had not accepted it. We press to accept that new value, as shown in Figure 38.
Figure 39	For Figure 39, we move down to the open line via the key. Then we use the key to move to the input line. We enter a new value, 3.0125, by pressing . We accept that value by pressing , and then we shift over two columns by using the key sequence. Note, again, that although the TABLE display gives a truncated version of the value, we can see the full approximation of the highlighted value in the input line.