# How do I find the asymptotes of f(x)= (- 4x-x^2)/(2 + x^2)?

May 5, 2018

Below

#### Explanation:

There is no vertical or oblique asmpytote. However, there is a horizontal asymptote

To find the horizontal asymptote, you have:

${\lim}_{x \to 0} \frac{- 4 x - {x}^{2}}{2 + {x}^{2}}$

${\lim}_{x \to 0} \frac{- \frac{4}{x} - 1}{\frac{2}{x} ^ 2 + 1}$

${\lim}_{x \to 0} \frac{- 0 - 1}{0 + 1}$

${\lim}_{x \to 0} - 1$

$y = - 1$ is your horizontal asmyptote

graph{(-4x-x^2)/(2+x^2) [-10, 10, -5, 5]}

Looking at the graph, you can tell that it is approaching $y = - 1$ from both ends of the graph