Find all the vertical asymptotes (if any)of the graph of the function .
D) ,
E)no vertical asymptotes

Question

Find all the vertical asymptotes (if any)of the graph of the function  . ​
D) , 
E)no vertical asymptotes

Quizplus · Accepted Answer

A vertical asymptote occurs when the denominator of the function equals zero and the numerator does not. In choice D, the denominator is (x - 3)(x + 1), which equals zero when x = 3 or x = -1. The numerator is not equal to zero at these values, so there are vertical asymptotes at x = 3 and x = -1. Choices A, B, and C have denominators that do not factor, so there are no vertical asymptotes. Choice E implies that there are no vertical asymptotes, but this may not be true without additional information about the function.

Find All the Vertical Asymptotes (If Any)of the Graph of the Function