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**.

[Press here to see animation again!]

- 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.
- Press the GRAPH key and then pick
**y(x)=**by pressing the F1 key. - If necessary, keep pressing the F4 key until only
**y1=**appears on the screen. - 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. - The range settings for the initial graph above is
**[-2, 5]**×**[-2, 5]**: - Pick
**GRAPH**from the menu by pressing the F5 key. - You will then see the graph of the greatest integer function:
- Again pick
**y(x)=**by pressing the F1 key. - At the prompt
**y1=**, type in**int x + int(- x)**and press the ENTER key.

- Pick
**GRAPH**from the menu by pressing the F5 key. - 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**.