# How do you find all the asymptotes for function #(x^2+1)/(x^2-9)#?

##### 1 Answer

This function has vertical asymptotes at

#### Explanation:

For the horizontal asymptote, note that the rational function

For the vertical asymptotes, the best thing to do initially in general is to factor the numerator and denominator as much as possible and cancel any common factors. In this case, the numerator cannot be factored further over the real numbers and the denominator has no common factors with the numerator:

Because nothing cancels, the vertical asymptotes will occur at the values of

Here's a picture of the graph of this function:

graph{(x^2+1)/(x^2-9) [-20, 20, -10, 10]}