Graph, Trace, Window, Plot

This page is devoted to presenting, in a step by step fashion, the keystrokes and the screen images for doing a some of the examples from Chapter 1 section 2 of the text on a TI-83. The example used is to find the best fit line for the data given as

Mode Screen	First we want to be sure that the calculator has the correct mode settings. To do this, use to display a screen similar to Figure 1. All of the options on the left, and only the options on the left, should be highlighted. If your screen does not appear like this, then you should fix it. Use the cursor control keys to move up and down, left and right on the screen. Then use the key to select the desired option. To get out of the review of modes, press the .
Figure 1	We will start with Example 1 from the book: Determine whether (a) (2,13) and (b) (-1,-3) lie on the graph of y=10x-7. To do this we will set the graphing function Y1 to be 10X-7. Press the key to open the screen in Figure 1.
Figure 2	We enter the desired function using the keys. Then, we can complete the task and move to get a graph of this line by pressing the key.
Figure 3	Here is a graph of the function y=10x-7 but we cannot really see if the two given points are on the line.
Figure 4	The caluclator has a feature that can help us here, namely the TRACE feature. Enter this by pressing the key. THis should put the calculator into the trace mode and display the modified graph as in Figure 4. Note that there is a blinking (well, not blinking on the web page but blinking on the screen) cursor on the line. Fruthermore, at the top of the screen the calculator shows us the particular function being traced, in this case Y1=10X-7. The coordinates of the point being highlighted appear at the bottom of the screen so we can see that the cursor is at the point (0,-7).
Figure 5	We can move that cursor to the point that has its x-coordinate being 2 by pressing the key to generate Figure 5, and then pressing the key to move to Figure 6.
Figure 6	The cursor has disappeared in Figure 6 because the point (2,13) is off the screen. However, the calculator has confirmed that the point (2,13) is on the line y=10x-7.
Figure 7	To check on the other point (-1,-3), we type to generate Figure 7. We follow that with key to move to Figure 8.
Figure 8	Reading the coordinates at the bottom, we see that the point (-1,-17) is on the line. That means that (-1,-3) is not on the line, something we should have noted from inspection of the graph since the line crosses the y-axis at (0,-7) and moves down and to the left from there. (-1,-3) is up and to the left of the y-intercept.
Figure 9	Without losing our original function, we can enter the function of Example 2, namely, y=7-3x, into the calculator. Press the key to return to the Y= screen as shown in Figure 9. Note that the screen capture that produced Figure 9 happened to catch the blinking cursor as a black rectangle that is covering the 1 of the 10X-7.
Figure 10	To enter the new function use the key to move to the Y2= line, then enter the function using the keys , producing the image shown in Figure 10.
Figure 10a	Pressing the key displays the graph of Figure 10a, with both lines on it.
Figure 11	Return to TRACE mode using the key. Note that the calculator is again tracing the first function, Y1=10X-7.
Figure 12	Press the key to change the trace to the next function, in this case Y2=7-3X. We see that the cursor is at the point (0,7).
Figure 13	Press the key to move to the next pixel position to the right on the graph. The highlight moves a,d the coordinates change. This is the point (.21276596,6.3617021). That is not a pretty pair of values, but it is on the line. We might want to find a nicer spot so we can continue to press the key until we ge the screen shown in Figure 14.
Figure 14	We are getting close to having the x value be 1.
Figure 15	Press the key one more time and we are at the display in Figure 15. Here we have moved beyond having x=1.
Figure 16	As demonstrated before, we can have the calculator evaluate the function at a particular point while in the TRACE mode by entering that x value. To get Figure 16 we press the key.
Figure 17	Complete the process by presing the key. In FIgure 17 we see that the point (1,4) is on the graph.
Figure 18	To find the coordinates of the point that has the x-coordinate as 2, we press . This produces Figure 18 where we find that (2,1) is on the line. We could enter even more x-values and for each one the calculator will give us the corresponding y-coordinate. We would just have to write down each pair as we generate it. Perhaps there are other ways to generate such lists of values.
Figure 19	One way to do this is to generate a list of x values and then compute the corresponding list of y values. Press the key to open the screen shown in Figure 19. As it opens the first option, Edit, is highlighted. Press the key to move to Figure 20 where we can edit the lists.
Figure 20	Figure 20 shows the screen as it will appear if there are no values already in the L1, L2, and L3 lists. The screen also shows that the calculator is waiting for us to give it a value to put as the first item in L1.
Figure 21	Press to indicate that we want that first item to be -1.
Figure 22	Complete the entry by pressing the key. The -1 appears in L1 and the calculator is ready to accept a value for the second item in L1.
Figure 23	We enter the rest of the values by pressing in order to produce Figure 23.
Figure 24	At this point we press the key to move to the second column, L2.
Figure 25	We want to have the calculator compute values for L2. We use the key to move the highlight out of the list items and onto the list name, L2. Note that at the bottom of the screen the calculator now asks for a definition of L2.
Figure 26	for Figure 26 we have entered the desired expression by using the key sequence. Note that we are nomaking reference to the definition in Y2. Rather we are entering the expression again, this time using L1.
Figure 27	We press to move to Figure 27 where the values of L2 have been computed and displayed. Here, in one screen, we have all the values that we need for Example 2. There is a problem with this, however. The values have been computed and are no longer tied to either the value in L1 nor to the definition that we entered. To see this we start by pressing to move the highlight back to the first column as shown in Figure 28.
Figure 28	We can demonstrate the problem by changing one of the values in the first column. The first value is highlighted so we might as well change that one.
Figure 29	Press the kys to enter -5 at the bottom. To move to Figure 30, press the key.
Figure 30	Note in Figure 30 that the first value in the L1 list has indeed changed, but that such a change had no effect on the corresponding value in the second column.
Figure 31	To start to correct this we use the key to move to the second column and then the sequence to put the highlight at the heading of the second column, L2. Note that the bottom of the display shows the definition of L2. It is no longer the 7-3L1 that we entered in Figure 26. It is now just the list of values.
Figure 32	We replace that list of values with a retyping of the definition, 7-3L1.
Figure 33	Press to produce Figure 33. Again, at this point the values in the two lists represent the coordinates of points on the line.
Figure 34	We can actually plot the points identified in Figure 33. To do this we need to be sure that the calculator is set to plot points where the x-coordinate is in L1 and the y-coordinate is in L2. We press the keys to open the STAT PLOTS screen shown in Figure 34. The first of the STAT PLOTS is highlighted and it shows that Plot1 is Off and that Plot1 is already set to plot points using L1 and L2. Because it is currently selected, to get to the detail of Plot1 we press the key.
Figure 35	Figure 35 shows the screen as we have moved to the details of Plot1, with the exception that you cannot see the blinking cursor. IT happens to be on the ON option. To select the option press the key. That will move us to Figure 36. highlighted
Figure 36	Now the ON option is selected. The blinking cursor is still on that option. We can finally move to the graph by pressing the key.
Figure 37	Figure 37 is similar to Figure 10a, but with the addition of the points we have plotted. You might note that out first point, from Figure 33, (-5,22), is not shown because it is off the displayed window of the graph.
Figure 38	To get to Figure 38 we press the key to move back to the TRACE feature of the calculator. When we did this before, in Figure 4 and Figure 11, the calculator started the TRACE looking at the first function, Y1=. This time it has started the trace looking at Plot1 represented in the upper left corner of the screen by P1:L1,L2. Within that Plot1, the trace starts with the point at X=-5 and Y=22, which, as noted above, is off the screen. THese values are given at the bottom of the screen.
Figure 39	Press the to move to the next point of Plot1, namely (0,7). Note how the values change at the bottom of the screen, and, since that point is on the screen, there is now a flashing highlight on that point.
Figure 40	The fact that we are missing one of our plotted points is a little inconvenient. THe TI-83 provides a feature to change the window so that all of our plotted points will be on the screen. We press the key to open the ZOOM window in Figure 40.
Figure 41	The option that we want, ZoomStat, is not displayed in Figure 40, so we use the down cursor button, , to move the highlight down to option 9 as shown in Figure 41. Then, press the key to perform the highlighted option.
Figure 42	Having changed the window by using the ZoomStat feature in Figure 41, the calculator redisplays the plots and graphs, but this time with the window settings such that all of the Plot1 points are displayed on the screen. A consequence of the previous action is that the graph looks different in that the lines are not nearly as steep as they were before. The reason for this is that the range4 of the y-axis has been increased dramatically to allow for the point (-5,22). That compresses the y-axis, effectively squishing down the graph to fit into the window.
Figure 43	We can look at the WINDOW settings by pressing the key. The settings in Figure 42 are the result of our earlier action of using the ZoomStat feature. Note that the x values are spread actross the wide part of the screen from -5.9 to 4.9. The y values are spread across the narrow part of the screen from -9.59 to 26.59.
Figure 44	Of course, we can change these values. We do this by using the cursor keys to move through the fields and we enter new values as we see fit. One thing to keep in mind as we do this is the actual number of pixels (picture elements, the dots that make up the screen) on the calculator. There are 95 horizontal pixels across the calculator and 63 vertical pixels from top to bottom on the display. We could number the pixels from 0 to 94 across and 0 to 62 up and down. The 94 and 62 values are important to remember. [For a more in depth look at pixels on the TI-83 see the Pixels on TI-83 page.] Thus, if we choose a span on the x values that is some multiple of 94 then we will have some nice even steps across the screen. In this case, in Figure 44, we have selected -10 as the Xmin value and set 18.2 as the Xmax value. Thus, the horizontal spread is 28.2 or 394/10. As we will see, each step across the screen will represent a change of 3/10 or 0.3 unitls. The Ymin* is set as -10 and Ymax is set to 27.2. This represents a spread of 37.2 or 6*62/10. As such each step up and down on the screen will represent a change of 6/10 or 0.6 units. The Yscl value was changed to 2 so that the tick marks on the y-axis area spread out a bit. We see in Figure 42 that these tick marks pile up on each other.
Figure 45	Press the key to return to the graph, this time with new WINDOW settings. All of the points are still here and again the slope of the lines has changed. We might note that the changes that we made in Figure 44 represent little change in the spread of the y values from what they were in Figure 43. However, the spread of the x values has increased significantly. Thus we are squeezing more x values onto the screen. In effect, we are squeezing the screen horizontally, thus making the lines look steeper. Also note the nice spread of the tick marks on the y-axis because of the change that we made to the Yscl value.
Figure 46	For Figure 46 we turn on the TRACE feature by using the key. As expected the TRACE feature again starts with the Plot1 values.
Figure 47	Remember that the up and down cursors are used to move from one plot ot graph to the next. Pressing the will take the TRACE to the graph before the Plot1, namely, Y2=7-3X. Note the nice values that we hit. Such nice values are the consequence of our choices for the Xmin, Xmax, Ymin, and Ymax values.
Figure 48	Pressing the key once moves us to a different point and, as anticipated, the x value has dropped by 0.3 units.
Figure 48a	There is yet another way that we can use the TI-83 to help with Example 2. First, we return, in Figure 48a, to the Y= screen by pressing the key. We see our definitions for Y1 and Y2 here.
Figure 48b	Then we want to look at the TBL SET screen, so we press the keys to get Figure 48b. The settings shown here mean that when we move to the TABLE screen the independent vaiable, X, will start with a value of 0, it will increase by 1 for each row of the table, and that the values of the independent variable and the dependent variable will automatically be displayed.
Figure 48c	For illustration, we will set the TblStart value to -2. Then, press the keys to move to the TABLE screen, shown in Figure 48d.
Figure 48d	In this image we see that the TI-83 has created a table of values for X, Y1, and Y2. The X values, as the independent variable, start at -2 and increase by 1 with each row. The values in the Y1 column are calculated based upon the function definition for Y1 that we saw in Figure 48a. The values in the Y2 column are calculated based upon the function definition for Y2 that we saw in Figure 48a. Thus, in just a few steps, we have lots of values for the coordinates of points on the two functions that we have been using.
Figure 48e	Because all of this is automatic, we can use the cursor key to move up the table. Press to move up one row. Note that the new values for all three variables are automatically computed.
Figure 48f	Naturally, we could use the key to move down the list. If we do this a number of times we can get to the row for X=8 as shown in Figure 48f. Note also that in Figure 48 the first X value is 2.
Figure 48g	Pressing to return to the TBL SET screen in Figure 48g, we see that by changing the screen in Figure 48f as we did the calculator has changed the TBL SET settings to have the TblStart value now be 2.
Figure 48h	To get to Figure 48h we bring the blinking cusor down to the Indpnt line and move it over the Ask option, and then press the key. In this mode the calculator will ask us for values for the independent variable, X.
Figure 48i	Returning to the TABLE screen via the key sequence, we see in Figure 48i that the values are no longer generated by the TI-83. Instead, the TI-83 is waiting for us to enter the desired values for the independent variable.
Figure 48j	If we press the key the calculator display esponds as in Figure 48j.
Figure 48k	Pressing the key moves the calculator display to Figure 48k. Now the value 5 has been added to the table and the corresponding values for Y1 and Y2 have been added to the table. These values have been comuted using the definitions of Y1 and Y2 that we saw in Figure 48a in the Y= screen.
Figure 48l	To demonstrate a bit more of the TABLE feature, Figure 48l shows the results of adding new values to the X column of the table, namely, -1, -6, 3, 4, and 5. Since we decide the values for the X column there is no particular order or spacing of the values and values can be repeated. For each value in the X column, the TI-83 computes the corresponding value in the Y1 and Y2 columns. The automatic feature, and the fact that we are using the definitions of Y1 and Y2 for our computations, is an advantage over the use of L₁, L₂, STAT -- EDIT, and STAT PLOT demonstrated above. The disadvantage of using the TABLE approach is that we cannot graph the TABLE points automatically.
Figure 49	To move away from Examples 1 and 2 and onto Example 3, we should really turn off the exisiting plot and then enter a new definition for the new function of Example 3. Press To get tot eh STAT PLOT screen shown in Figure 49. We see here that Plot1 is On. Since Plot1 is highlighted, press to move to the Plot1 screen of Figure 50.
Figure 50	This is the current setting of Plot1.
Figure 51	Move the highlight to the Off option and then press to make Off the chosen option.
Figure 52	Press the key to move to the Y= screen, shown in Figure 52.
Figure 53	Press the keys to get to Figure 53. Note that the DEL key was needed because we still had the 7 left on the line from the earlier value.
Figure 54	Pressing the key deletes the entire definition of Y2 in Figure 54.
Figure 55	Now we are ready to graph the function. Press the key to do so. The result is shown in Figure 55.
Figure 56	We go to the TRACE feature by pressing the key. You might note that the X value selected was 4.1, the same initial X value that we found in Figure 47. This is due to the fact that we have not changed the WINDOW settings that we last saw in Figure 44.
Figure 57	Indeed, if we press the key we see the highlight move to the X=3.8 value, just as in Figure 48.
Figure 58	Although moving the cursor left and right gives us nice values for X, we are moving in steps of 0.3. From 4.1 we are not going to get to the value of 4 in that way. Fortunately, we can still just press the key to enter that value, as in Figure 58.
Figure 59	Press the key and the TRACE feature responds by giving Y=14 and highlighting the point holding (4,14) on the curve.
Figure 60	Our values in L1 and L2 have not changed. We press to move to and through the STAT screen and arrive at Figure 60.
Figure 61	For Figure 61 we have changed the values stored in L1
Figure 62	For Figure 62 we have used the key to move to the L2 column and then the key, repeatedly, to move the highlight to the heading L2.
Figure 63	In Figure 63 we have entered the expression for our function, subsituting L1 for X. The key strokes for this are .
Figure 64	To move to Figure 64, press the key and the TI-83 computes and displays the new values for L2.