# What are the asymptotes for #f(x) = (x^2 -1)/(2x^2 + 3x-2)#?

##### 1 Answer

Vertical asymptotes:

Horizontal asymptote:

#### Explanation:

We can have:

1] Vertical asymptotes; which are vertical lines at

To make the denominator equal to zero you can solve it as a 2nd degree equation:

using the Quadratic Formula you get:

these two are the equation of your two vertical asymptotes.

2] Horizontal asymptote; which are horizontal lines that again cannot be crossed by the graph of your function. Your function instead tends to get as near as possible to them.

To find them you look at the behaviour of your function for **Limit** :

rearranging and taking the limit we get:

(remember that as

Your horizontal asymptote will then be:

Graphically you can see them as:

graph{(x^2-1)/(2x^2+3x-2) [-10, 10, -5, 5]}