# How do you find the vertical, horizontal and slant asymptotes of: f(x)= (x)/(4x^2+7x+-2)?

Dec 7, 2016

For + sign equation - Horizontal:$\leftarrow y = 0 \rightarrow$; and vertical : $\uparrow x = - 1.39 \mathmr{and} x = - 0.34 \downarrow$. For $-$ sign- Horizontal: larr y=0rarr; and vertical: uarr x= -2 and x=1/4 darr.

#### Explanation:

The zeros of the denominator $4 {x}^{2} + 7 x {+}_{2}$ are

$- 1.39 \mathmr{and} - 0.34$ for + sign $\mathmr{and} - 2 \mathmr{and} \frac{1}{4}$ for - sign.

For the straight lines x = these values, $y \to \pm \infty$.

Also, as x to +-oo, y to 0.

graph{y(4x^2+7x+2)-x=0 [-20, 20, -10, 10]}
graph{y(4x^2+7x-2)-x=0 [-10, 10, -5, 5]}