Problem:
Using the TI-86 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:

1. Press the GRAPH key and then pick y(x)= by pressing the F1 key.
2. If necessary, keep pressing the F4 key until only y1= appears on the screen.
3. At the prompt y1=, type in

int x

and press the ENTER key. int(x) is the greatest integer function on the TI-86. You can either type in "int" (small case please) or you can find int by pressing 2nd MATH, then F1, and then F4.

4. Go to the WINDOW menu by pressing 2nd M2.
5. The WINDOW 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

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.

Constructed with the help of Chris O'Brien.