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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
Remember that vertical asymptotes occur when you have some kind of “non-zero over zero” type situation happening at a point.
Try finding all the domain restrictions as a starting point if you are having trouble.
Determine if the following function has any vertical asymptotes. What is the sum of the values which have vertical asymptotes?
[correct] 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
Remember that vertical asymptotes occur when you have some kind of “non-zero over zero” type situation happening at a point.
Try finding all the domain restrictions as a starting point if you are having trouble.
Specifically, start by factoring the top and bottom functions completely.
Next cancel any common factors to see which restrictions remain. Take limits as approaches those values.
Determine if the following function has any vertical asymptotes. What is the sum of the values which have vertical asymptotes?
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!
Business Calculus One