# How do you find the asymptotes for #f(x) = (2x^2 + 1) / (x^2 - 4)#?

##### 1 Answer

The vertical asymptotes are

#### Explanation:

Vertical asymptotes occur where

*Factor*

*Set each factor equal to zero*

*Solve for x*

The vertical asymptotes are

Horizontal asymptotes are found by comparing the degree of the denominator to the degree of the numerator.

If the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is

If the degree of the denominator is equal to the degree of the numerator, the horizontal asymptote is the leading coefficient of the numerator divided by the leading coefficient of the denominator.

In this example, the

If the degree of the denominator is less than the degree of the numerator, there is an oblique asymptote. This example does not have an oblique asymptote.