How You Can (And Should) Get More Practice!

Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for you.

Worked Out Examples Problem Videos

The following video may be helpful when trying to solve the problems in this practice section. Note that you may skip to the end of the video to get completion credit for this page if you don’t need to watch them.

_

Practice Problems

Theoretically Easier Difficulty Problem

To find horizontal asymptotes, you want to take the limit as approaches infinity (for the right HA) and negative infinity (for the left HA).
For rational functions with polynomials on the top and bottom, it can help to divide by a “suitable power of ”. Commonly dividing by the second highest power of works well, but sometimes you need to divide all terms by the highest power of .
Determine if the following function has any horizontal asymptotes. Left Horizontal Asymptote (if there is no asymptote, enter DNE)

Right Horizontal Asymptote (if there is no asymptote, enter DNE)

Theoretically Harder Difficulty Problem

To find horizontal asymptotes, you want to take the limit as approaches infinity (for the right HA) and negative infinity (for the left HA).
Determine if the following function has any horizontal asymptotes. Left Horizontal Asymptote (if there is no asymptote, enter DNE)

Right Horizontal Asymptote (if there is no asymptote, enter DNE)