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

##### 2 Answers

Vertical asymptotes:

Horizontal asymptotes:

No oblique asymptotes.

#### Explanation:

You have vertical asymptotes where the function is not defined, and this function is not defined where its denominator equals zero. So, we have

which means

As for horizontal asymptotes, you have them if the limits as

The presence of horizontal asymptotes excludes the one of oblique asymptotes.

has vertical asymptote at

#### Explanation:

with exclusion

When

When

As

So

graph{(2x-4)/(x^2-4) [-10, 10, -5, 5]}

It is possible for a function to have two horizontal asymptotes, or two oblique asymptotes, or one of each.

For example, the function

graph{arctan(x) [-10, 10, -5, 5]}

Consider also

This slightly messy function has horizontal asymptote

graph{(x+abs(x))/2+1/(x^2+1) [-8.89, 8.885, -4.434, 4.45]}