Introduction to Tables on the TI-83

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

Figure 1	We enter the TBLSET screen by pressing first the key and then the key. The result is shown in Figure 1, although the highlighted areas and values may be different on a different calculator. Note that the calculator used to generate Figure 1 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 2	We change the value to be -3 by pressing the keys. This leaves the screen as is shown in Figure 2.
Figure 3	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 3.
Figure 4	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 both Figure 2 and 3 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 4a.
Figure 4a	Here we can see that the Auto setting has been selected. Now we can move down to the Depend setting by pressing the key which will move the highlight to the Auto value on that line. This setting will control how the calculator works with the dependent variables, the y's. We say that the y-variables are dependent because once we have chosen a value for the independent variable, x, the function determines the value that we need to have for the dependent variable. Again, we want the calculator to function automatically, to calculate function values immediately, without our intervention. The current setting is Ask, but the highlight will be on Auto. Therefore, we can press the to make Auto the chosen value.
Figure 5	In Figure 5 we see the screen with all the values set as we want them. At this point we are done with the TBLSET screen. Now it is time for us to enter the functions that we want to use in our table. To do this we will move to the Y= screen.
Figure 6	In Figure 6 we have moved to the Y= screen by pressing the key. The display in Figure 6 shows that no functions are defined in the calculator. If that is not the case then you will want to clear each of the functions defined so that the screen looks as shown in Figure 6. You can use the CLEAR key and the cursor keys to point to and clear any functions that were defined, and then to move back to the first function.
Figure 7	For Figure 7, 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 subscript 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 7.
Figure 8	We move from Figure 7 to Figure 8 by pressing the key. The calculator responds with the table shown in Figure 8. The first column has values for x, the independent variable. Those values start at 3, the values that we assigned to . The x values increase by 0.5 as we move down the first column. That change between x values is exactly the value that we assigned to . The values in the second column, headed by Y1, are the values of the expression 2X+1, for each of the corresponding x values in the first column. The values in the third column, headed by Y2, are the values of the expression X2-4, for each of the corresponding x values in the first column. The table is showing us the 7 independent values (selected by knowing the and values), and 7 values for the first expression (under the Y1 heading), and 7 values for the second expression (under the Y2heading). At the bottom of the screen, in larger characters, the calculator displays the value that is highlighted above, in Figure 8 this is the X=-3 item.
Figure 9	We use the key six 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 10	Figure 10 shows a new row for the table. We lost the old top row. The viewable part of the table remains seven 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= screen are used to create new dependent values in the other columns.
Figure 11	To change from Figure 10 to Figure 11 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 12	Figure 12 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 13	We can press to return to the Y= screen. Here we will use the cursor keys to move down to the Y3= line. There we will enter another function, h(x)=(x+2)(x-1).
Figure 14	We return to the TABLE screen by pressing the keys. It does not look like the display has changed from what it was in Figure 12. Where is the new function? We will need to move the cursor to the right to see it.
Figure 15	For Figure 15 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 16	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 17	We have seen, back in Figures 12, 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 16 we were at the top of a dependent column. We move to Figure 17 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 18	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 18 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 19	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 19. We change the "1" to a "3" by pressing the key. The result is seen in Figure 20.
Figure 20	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 21.
Figure 21	The function definition for Y3 has been changed and now new values are deiplayed in this column. Let us return to the Y= screen so that we can verify that the function has changed there too. We move back to the Y= screen by pressing the key.
Figure 22	Here, in Figure 22, we have returned to the Y= screen. We can see that the third function definition has changed.
Figure 23	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 23.
Figure 24	We return to the TABLE screen in Figure 24 by pressing . 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 25.
Figure 25	We can see that the value for has changed. It will always be the value at the top of the independent column. In Figure 12 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 26	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 26.
Figure 27	We return to the TABLE screen by pressing . Note the changes in the displayed values.
Figure 28	We will return to the TBLSET screen to look at values assigned to Indpnt and Depend. Again we move to the screen by pressing . This time we will use the key to move the blinking cursor down to the Depend 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. Then 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 28.
Figure 29	Let us return to the TABLE screen by pressing . The result is shown in Figure 29. All of the previously automatically displayed dependent values have disappeared.
Figure 30	We can use the cursor keys to move the highlight to any cell in a dependent column. This was done in Figure 30.
Figure 31	Then, if we press the key, the calculator will fill in that cell with the appropriate value.
Figure 32	Figure 32 represents having moved to yet another cell in a dependent column and having pressed the key to display that functional value.
Figure 33	We can press to return to the TBLSET screen in Figure 33.
Figure 34	This time we will position the blinking cursor onto the Ask field in the Indpnt line and then we will select that option by pressing the key. The display show appear as in Figure 34.
Figure 35	Pressing the keys returns us to the TABLE screen, shown in Figure 35. Now we have no values displayed on the table. The cursor is positioned in the independent variable column.
Figure 36	With the Indpnt value set to be 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 36, we have pressed the keys. The value, -2.25, appears at the bottom of the screen.
Figure 37	To accept the value entered in Figure 36, we press the key. The calculator places the value into the independent variable column, and moves to accept another x-value. This is shown in Figure 37.
Figure 38	We have used the cursor keys to move the highlight to the top position of the Y1 column in Figure 38.
Figure 39	If we now press the key, the calculator displays the computed value of the first function based on the corresponding value of the the independent variable.
Figure 40	Pressing the keys returns us to the TBLSET screen. This time we will move the cursor back to the Auto option in the Depend line, and we will press to select that option. The result is shown in Figure 40.
Figure 41	To move back to the TABLE screen we press . This new screen is shown in Figure 41. Note that the value of the second function is computed and displayed. The Auto setting on the Depend line causes the calculator to automatically compute and display values for the dependent variables each time an independent value is added or is changed. We can see this by adding another independent value.
Figure 42	In Figure 42, we have pressed the key to move to a new independent value, and we have pressed the key to set that value to be 5.
Figure 43	We complete the entry of the value in Figure 42 by pressing the key (or we could press the cursor down key). The result is twofold. FIrst, we move down, ready to accept another new independent value. And, second, the values of the dependent variables associated with the value we just entered, 5, are automatically computed.
Figure 44	We will complete this sequence of screens by looking at the effect of entering a lengthy number. We will add yet another independent value, namely, 2.782456. We can see this value at the bottom of Figure 44.
Figure 45	We complete the entry of 2.782456 in Figure 44 by pressing the key. The result is in Figure 45. Note that the the value displayed in the table is rounded off to 2.7825. There just is not enough room in the table to show all of the digits.
Figure 46	For Figure 46 we have moved the cursor to the first dependent variable for our new row. Although the table gives the value as 6.5649, the display at the bottom of the screen gives the longer value, 6.564912.
Figure 47	Again, moving the cursor to the right to look at the value in the third column, the table shows 1.4921 whereas the bottom of the display gives the computed value as 1.49206139194.