# How do you find the asymptotes for f(x)=x /( 4x^2+7x-2)?

Apr 29, 2016

vertical asymptotes x = -2 , $x = \frac{1}{4}$
horizontal asymptote y = 0

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation/s set the denominator equal to zero.

solve : 4x^2+7x-2=0 → (4x-1)(x+2)=0

$\Rightarrow x = - 2 , x = \frac{1}{4} \text{ are the asymptotes }$

Horizontal asymptotes occur as ${\lim}_{x \to \pm \infty} , f \left(x\right) \to 0$

If the degree of the numerator < degree of the denominator then the equation is always y = 0
graph{x/(4x^2+7x-2) [-10, 10, -5, 5]}