# How to find the asymptotes of f(x) =(9x^2 – 36)/( x^2 - 9) ?

Jan 11, 2016

Vertical asymptotes occur when the denominator equals $0$ ...

#### Explanation:

Vertical Asymptotes :
${x}^{2} - 9 = 0$
${x}^{2} = 9$
$x = 3 \text{ or } x = - 3$

Horizontal Asymptotes :
Find the highest exponents in the numerator and denominator, then divide ...

$y = \frac{9 {x}^{2}}{x} ^ 2 = 9$

So, $y = 9$ is the horizontal asymptote.

Here is a graph. The dotted lines are the asymptotes ...

Hope that helped