# How do you find the asymptotes for g(x)=(x+7)/(x^2-4)?

Jan 12, 2016

Vertical aymptotes: $x = \pm 2$
Horizontal asymptotes: $y = 0$

#### Explanation:

Vertical asymptotes:

These occur when the denominator equals $0$.

${x}^{2} - 4 = 0$

$\left(x + 2\right) \left(x - 2\right) = 0$

$x = - 2 \textcolor{w h i t e}{s s s} \text{or} \textcolor{w h i t e}{s s s} x = 2$

Horizontal asymptotes:

Since the degree of the denominator is larger than the numerator, the horizontal asymptote will be at $y = 0$.

Graphed:

graph{(x+7)/(x^2-4) [-11.01, 11.49, -5.9, 5.35]}