# How do you find the horizontal asymptote for  g(x) = (3x^2) / (x^2 - 9)?

Nov 14, 2015

Solve for ${x}^{2} - 9 = 0$

#### Explanation:

In order to find the horizontal asymptote of a function, you have to solve it's denominator, while in order to find the vertical asymptote, you'll have to solve $y = \frac{a}{c}$, such that $y = \frac{a x + b}{c x + d}$. Note, the principles hold true for all degrees of $x$, so you can also use these two formulae if your function has a squared, or cubic, $x$.

To find the horizontal asymptote of $g \left(x\right)$, solve the denominator part. Hence, ${x}^{2} - 9 = 0$
${x}^{2} = 9$
${x}^{2} = {3}^{2}$
so, $x = 3$

Therefore the horizontal asymptote of $g \left(x\right)$ is $x = 3$, or $x - 3 = 0$.