Hello, thereddevils!

Sketch the graph for each of the following functions, showing clearly the asymptotes.

I know that are asymptotes, as they make the function undefined. You're right . . . Those are the *vertical* asymptotes.

We must also look for horizontal asymptotes.

They occur when has a finite value.

We have: .

Divide top and bottom by

So we have: .

Therefore, (the -axis) is a horizontal asymptote.

Code:

| : :*
| : :
| *: : *
| : : *
| : : *
| * : : *
--------------------+---:-----------:--------------------
* * : :
* *| : * :
* * | : * * :
* | : * * :
| : :
| : * * :
| : :
| : :
| :* *:
| : :