### Home > APCALC > Chapter 1 > Lesson 1.2.5 > Problem 1-90

y =

y =

y =

y =

Since (*x* − 2) cancelled out, *x* = 2 is the location of a hole.

Now simplify. And notice what was cancelled out.

The *y*-value of the hole can be found by evaluating the simplified function at .

did not cancel out, so

*and*

*are vertical asymptotes.*

Now find the end behavior. You can long divide or use an approach statement: ,

*and as*

*,*

*. There is a horizontal asymptote at*

*.*

Last but not least, investigate what is happening in the middle, by exploring the holes and vertical asymptotes. Use the simplified equation:

Use the eTool below to view the steps for graphing the first equation.

Click the link at right for the full version of the eTool: Calc 1-90 HW eTool