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

Simplify the following functions. *Without a calculator*, sketch each graph, showing roots, holes and asymptotes. Then, state the domain in parts (a) and (b) using **interval** notation and the domain in parts (c) and (d) using **set** notation. .

Since is the location of a hole.

Now simplify. And notice what was cancelled out.

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

*.*

So the hole has a coordinate point of

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*