The user-friendly version of this content is available here.

The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.

This problem trains for: SAT-II.

How many asymptotes does the graph of the function have?

The rational expression can be written as:

Therefore, as x becomes infinitely large, the function becomes infinitely close to the line:

which is a oblique asymptote.

Also, when x gets infinitely close to 1, the function becomes infinitely large. Therefore, x=1 is a vertical asymptote.

The function has two asymptotes.