Problem:
Using the TI-85 graphing calculator, investigate graphically the behavior of the function

for values of x near 2. [[ x ]] denotes the greatest integer less than or equal to x.

Visualization

[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 the F4 key until only y1= appears on the screen.
4. At the prompt y1=, type in

int x

and press the ENTER key. int(x) is the greatest integer function on the TI-85. You can obtain int by using the catalog; this is shown in the animation above.

5. The range settings for the initial graph above is  [-2, 5] × [-2, 5]:

6. Pick GRAPH from the menu by pressing the F5 key.
7. You will then see the graph of the greatest integer function:

8. Again pick y(x)= by pressing the F1 key.
9. At the prompt y1=, type in

int x + int(- x)

and press the ENTER key.

10. Pick GRAPH from the menu by pressing the F5 key.
11. You will now see the desired graph which is shown in the animation above. You can see that f(2) = 0 and by zooming in you see that the value of f(x) for all other x near 2 is - 1.