# How do you find the asymptotes for F(x) = (-2x^2 + 1)/(2x^3 + 4x^2)?

Dec 8, 2016

Vertical: $x = 0 \uparrow \mathmr{and} \uparrow x = - 2 \downarrow$. Horizontal:$\leftarrow y = 0 \rightarrow$.
For visual effect, see the graph.

#### Explanation:

$y \to \infty$, as $x \to 0. y \to {+}_{\infty}$, as $x \to - 2$.

The line y=0, besides making x-intercepts $\pm \frac{1}{\sqrt{2}}$, is asymptotic

to two ( of the three ) branches of the graph, in the two opposite directions.

graph{2yx^2(x+2)+2x^2-1=0 [-10, 10, -5, 5]}