Introduction to Tables on the TI-86

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

Figure 1	In order to get to the TABLE SETUP screen, we need to open the TABLE menu. We do this by pressing the key. Figure 1 shows the TABLE menu at the bottom. The first item in the menu is TBLST. We perform that option by pressing the key.
Figure 2	The result is shown in Figure 2, although the highlighted area and values may be different on a different calculator. 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 change the value to be -3 by pressing the keys. 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. Therefore, we press the key to move to the field. We set this field to be .5 by pressing the keys, leaving the screen as in Figure 4.
Figure 5	Again, we move to the next field by pressing the key. This field, the Indpnt 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. Looking at Figure 2 through 4 we can see that the calculator shown here is currently set to be in Ask mode. We want to use the and settings to automatically generate independent values. Therefore, we will want to change this setting to Auto, the setting currently covered by the blinking cursor. Because the cursor is on Auto, we can select that value by pressing the key. We do that to move to Figure 6.
Figure 6	Here we can see that the Auto setting has been selected. In Figure 5 we see the screen with all the values set as we want them. At this point we are done with the TABLE SETUP screen. 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(x)= screen.
Figure 7	In Figure 7 we have taken the first step toward moving to the y(x)= screen, we have pressed the key to open the GRAPH menu at the bottom. We can see that the y(x)= option is in the first position of that menu. Pressing the key will select that option and move the display to that of Figure 8.
Figure 8	In Figure 8 the blinking cursor is in position for input of the first function definition.
Figure 9	For Figure 9, we enter the two function definitions that we want. We started with f(x)=2x+1 and g(x)=x2-4. Unfortunately, the calculator does not accept this notation. Instead, we write each of the functions using a y= notation. The different functions are noted by using a different indext for y. We start on the y1= line and type and then we use the to move to the y2= line. There we type to produce Figure 9.
Figure 10	We want to return to the TABLE menu. Therefore, we press the key. The change from Figure 9 to Figure 10 is the new menu at the bottom. We are now ready to actually see the table. Press to move to a display of the TABLE in Figure 11.
Figure 11	Finally, in Figure 11, we can see the table of values thatw e have set up. The first column holds values of the independent variable, x. These values are determined by the values that we assigned to and . The list of values starts with -3, the value assigned to . The subsequent values represent a change of 0.5 from the previous value, where 0.5 was the value assigned to . The values under y1 represent the value of the expression 2x+1 for each of the corresponding values in the x-column. We call y1 a dependent variable. We are free to choose the independent values, the x-values, but once they are chosen, the y-values are determined. The third column, headed by y2, represents the value of the expression x2-4 for each of the corresponding values in the x-column. At the bottom of the screen, in larger characters, the calculator displays the value that is highlighted above, in Figure 11 this is the X=-3 item.
Figure 12	We use the key five times to position the highlight on the 0 in the first column. Now that the highlight is at the bottom of the table, let us see what happens when we press the key again.
Figure 13	Figure 13 shows a new row for the table. We lost the old top row. The viewable part of the table remains six rows high. Each time we move down from the bottom row of the display, the calculator destroys the top row and creates a new bottom row. The value of is used to determine the new x value. The functions defined in the y(x)= screen are used to create new dependent values in the other columns.
Figure 14	To change from Figure 13 to Figure 14 we use the key to move the highlight back to the top of the independent values. What happens if we move up again (while we are at the top of the column of independent values)?
Figure 15	Figure 15 shows the TABLE screen after we have moved up, not jsut once, but five times. Again, the new rows of the table have been created for the new independent variable values and old rows, this time at the bottom of the screen, have disappeared. And, of course, new values have been created in the dependent variable columns.
Figure 16	In Figure 16 we are preparing to go back to the y(x)= screen so that we can add another function to the two already defined. We have pressed the key to change the menu to the GRAPH menu shown in Figure 16. Now a key will take us back to the y(x)= screen, shown in Figure 17.
Figure 17	Having returned to the y(x)= screen in Figure 17, we see that the blinking cursor is on top of the character 2 in the first function definition.
Figure 18	In Figure 18, we use the cursor keys to move down to the y3= line. There we will enter another function, h(x)=(x+2)(x-1).
Figure 19	Once we have entered the new function in Figure 18, we want to return to the TABLE screen so that we can see it in the table. We start the process by pressing the key to restore the TABLE menu, as shown in Figure 19.
Figure 20	Now we return to the TABLE screen by pressing the key. Figure 20 shows the reviesed table. It does not look like the display has changed from what it was in Figure 15. Where is the new function? We will need to move the cursor to the right to see it.
Figure 21	For Figure 21 we have pressed the key twice to move the cursor to the third column. We are still showing the independent variable, x, and two dependent variables, y1 and y2. Let us move to the right again by pressing the key again.
Figure 22	Having moved to the right, the calculator responds by displaying the y3 column. To do this, the calculator lost the y1 column and shifted the y2 column to the left. The three column display of the TABLE screen does not change. Rather the calculator always leaves the independent column in place and scrolls the dependent columns as needed.
Figure 23	We have seen, back in Figures 15, what happens when, starting with the highlight at the top of the independent column, the x column, we press the "cursor up" key. In that case, the table scrolled to reveal a new row. In Figure 22 we were at the top of a dependent column. We move to Figure 23 by pressing the key. This time the highlight moves up to the y3, and the definition of the function, y3=(x+2)(x-1) is given at the bottom of the screen.
Figure 24	We can shift the focus from the table of values to the definition of the function by pressing the key. This will change the display to that of Figure 24 whre the blinking cursor is at the bottom of the screen, on top of the first left parenthesis in the definition of the function. We are now in a mode where we can actually change the definition of the function.
Figure 25	We will change the definition of the function from y3=(x+2)(x-1) to y3=(x+2)(x-3). To do this we will use the key to move the blinking cursor to the "1". This is the condition shown in Figure 25. We change the "1" to a "3" by pressing the key. The result is seen in Figure 26.
Figure 26	Now that we have altered the function, we need to signal that we are done and that we want the calculator to return to the table. We do this by pressing the key to move to Figure 27.
Figure 27	The function definition for y3 has been changed and now new values are deiplayed in this column. Let us return to the y(x)= screen so that we can verify that the function has changed there too. We move back to the y(x)= screen by pressing the key to bring up the GRAPH menu, and then the key to select the y(x)= menu option.
Figure 28	Here, in Figure 28, we have returned to the y(x)= screen. We can see that the third function definition has changed.
Figure 29	While we are here, we can take the opportunity to change the second function. We use the and keys to place the blinking cursor over the "4" in the second function. Then we press to change the function as shown in Figure 29.
Figure 30	We return to the TABLE screen in Figure 30 by pressing key to open the TABLE menu, and then the . We can see that we are now displaying values that are using the altered second function. Recall that when we started this, back in Figures 1 and 2, we set the value of to be -3. Let us return to the TBLSET screen and see the values that are there now. We press to display Figure 31.
Figure 31	We can see that the value for has changed. It will always be the value at the top of the independent column. In Figure 15 we had moved up the independent column and had caused new rows to be displayed with new independent variable values. Each time we change the TABLE display to create new rows, the field is altered to reflect the new starting value. (This updating of takes place only when the Indpnt option is set to Auto.)
Figure 32	We can select a new starting value by entering it here. Let us return to the original -2.5 by pressing . This leaves the screen as in Figure 32.
Figure 33	We return to the TABLE screen by pressing . Note the changes in the displayed values.
Figure 34	We will return to the TBLSET screen to look at values assigned to Indpnt. Again we move to the screen by pressing . This time we will use the key to move the blinking cursor down to the Indpnt line. Once on that line, the blinking cursor will start by pointing to the Auto selection. We will move the blinking cursor to the Ask selection by pressing the key. This is the condition displayed in Figure 34.
Figure 35	We press the key to actually change the selection. The calculator responds by changing the background highlight to the Ask value, as is shown in Figure 35.
Figure 36	Let us return to the TABLE screen by pressing . The result is shown in Figure 36. All of the previously automatically displayed values have disappeared. We are now free to choose any independent value. When we do this the calculator will respond by displaying the associated dependent values.
Figure 37	With the Indpnt value set to Ask, we can place whatever value we wish into the independent variable column. The values that we choose need not conform to any pattern, nor do they have to be in any order. For this example, and in Figure 37, we have pressed the keys. The value, -2.25, appears at the bottom of the screen.
Figure 38	To accept the value entered in Figure 37, we press the key. The calculator places the value into the independent variable column, calculates and displays the associated dependent column values, and moves to accept another x-value. This is shown in Figure 38.
Figure 39	For Figure 39 we have entered a new independent variable value, namely, 4.21739. As we enter it, the number is shown at the bottom of the screen.
Figure 40	We have pressed to accept our new value. Figure 40 shows the new value and its associated dependent values in the table.
Figure 41	To achieve Figure 41 we used the key to return the cursor to the second row in the table, and then we used to move the highlight to the third column. We note that the table value that is displayed, and is highlighted, is 11.53638. This is as much of the value as the calculator will display in the actual table. However, that same value is displayed at the bottom of the screen to its full precision.