### Home > INT3 > Chapter 12 > Lesson 12.1.3 > Problem 12-40

Complete the table of values for

*f*(*x*) =. 12-40 HW eTool (Desmos). Desmos Accessibility Homework Help ✎ *x*–2

–1

0

1

2

3

*f*(*x*)Graph the points in the table. What kind of function does it appear to be? Why is it not correct to connect all of the dots?

Look for a pattern in the values in the table. What appears to be the relationship between

*x*and*f*(*x*)? Calculate*f*(0.9) and*f*(1.1) and add the points to your graph. Is there an asymptote at*x*= 1? If you are unsure, calculate*f*(0.99) and*f*(1.01) as well.Simplify the expression for

*f*(*x*). What do you think the complete graph looks like?

Doing the substitutions yourself will help you understand what is happening in this problem.

Notice that there is no point at *x* = 1.

The relationship between *x* and *y* appears to be linear. *f*(0.9) = 5.9, *f*(1.1) = 6.1.

Although the line is approaching the point (1, 6) from both sides, a point is not an asymptote.

Use the eTool below to complete the table.

Click the link at right for the full version of the eTool: INT3 12-40 HW eTool