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

$y = 0$ is a horizontal asymptote

#### Explanation:

Take the limit of $f \left(x\right)$ as x approaches $\infty$

$L i {m}_{x \to \infty} f \left(x\right) = L i {m}_{x \to \infty} \frac{x}{{x}^{2} + 4} = L i {m}_{x \to \infty} \frac{1}{x + \frac{4}{x}} = 0$

As $x \to \infty$ the function $y = f \left(x\right) \to 0$

then $y = 0$ is a horizontal asymptote.

God bless you.