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**.

- 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-86. You can either type in "int" (small case please) or you can find int by pressing 2nd MATH, then F1, and then F4. - Go to the
**WINDOW**menu by pressing 2nd M2. - The WINDOW 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
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.