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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.
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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)
Very nice! Don’t forget you can hit the green “Try another” button at the top right corner to get new versions of the problems for
unlimited practice!
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)
Very nice! Don’t forget you can hit the green “Try another” button at the top right corner to get new versions of the problems for
unlimited practice!
