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

Jan 7, 2017

horizontal asymptote: $y = 0$;
no vertical and slant asymptotes.

Explanation:

1) There are no vertical asymptotes since the domain is R

2) ${\lim}_{x \to \infty} \frac{x}{{x}^{2} + 4} = 0$, then there's a horizontal asymptote that's the x-axis

3) since there's a horizontal asymptote, there's not a slant asymptote