Problem:
Using the TI-85 graphing calculator, graphically determine whether the function

is continuous at x = 3.

Visualization:

Normally you should not expect that calculators would graph this function properly. However, the TI-85 graphing calculator allows you some control which provides a valid plot.

[Press here to see animation again!]

1. If you are not familiar with the graphing of functions on the TI-85, then first read the Initial Setup page from Little's Basic Guide to the TI-85.
2. Press the GRAPH key and then pick y(x)= by pressing the F1 key.
3. If necessary, keep pressing F4 key until only y1= appears on the screen.
4. 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 enter the not equal symbol by pressing 2nd TEST, MORE and then F1 keys. The menu obtained by pressing 2nd TEST also contains the symbol ==.
5. Press EXIT and the F1 keys to pick ZOOM from the menu. Press MORE and F4 keys to pick ZDECM from the menu.
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. Pick ZOOM by pressing the F3 key.
7. We will need to zoom out; pick ZOUT by pressing the F3 key.
8. You will now see a flashing tick mark in the middle of the screen and the coordinates of the tick mark at the bottom of the screen:

9. Using the arrow keys, move the tick mark 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.
10. 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.
11. Press the F3 key to pick FORMT.
12. Use the arrow keys to move the blinking cursor to DrawDot and press the ENTER key.
13. Finally, press the F5 key to pick GRAPH to get the last graph in the animation above.