Problem:
Using the TI-86 graphing calculator, graphically determine whether the function

is continuous at x = 3.

Visualization

1. Press the GRAPH key and then pick y(x)= by pressing the F1 key.
2. If necessary, keep pressing F4 key until only \y1= appears on the screen.
3. Be sure that PLOTS 1, 2 and 3 are turned-off.
4. At the prompt \y1=, type in the piecewise defined function

(x + 2)(x 3) + 2 (x == 3)

and press the ENTER key.

• This procedure will not work if we enter the quotient as stated in the first part of the definition of f above. However, since

the equation we entered is valid.

• You can find the == and the symbols in the TEST menu by pressing 2nd TEST then MORE if needed.
5. Press EXIT and the 2nd M3 keysi to go to the ZOOM menu. Then select ZDECM by pressing MORE and then F4.
Comment:
ZDECM is the command that makes much of this possible. With this command each pixel has width 0.1 and height 0.1.
6. Looking at the graph, one should determine that we need to zoom out. Do this by pressing MORE three times and then select ZOUT with the F3 key.
7. A blinking cursor will appear in the middle of the screen and the coordinates of the cursor will appear along the bottom of the screen:

8. Using the arrow keys, move the cursor as close to the intersection of the graph with the vertical line (which is the y-axis) as possible and press the ENTER key. The author obtained the following graph:

Comment:

You may get a different graph if your settings for xFact and yFact are different from the author's. The above graph was obtained by using xFact = yFact = 2. Recall that you can modify these factors from the ZFACT item on the ZOOM menu.
9. Note that we have the extraneous lines joining the point (3, 2) to the rest of the graph of the function. To eliminate these lines, press the EXIT and MORE keys so that FORMT appears on the menu.
10. Press the F3 key to pick FORMT.
11. Use the arrow keys to move the blinking cursor to DrawDot and press the ENTER key.
12. Finally, press the F5 key to pick GRAPH to get the graph.