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

##### 1 Answer

Apr 29, 2016

vertical asymptotes x = -2 ,

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 #

#rArr x = -2 , x=1/4 " are the asymptotes "# Horizontal asymptotes occur as

#lim_(x to +- oo) , f(x) 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]}