# How do you find vertical, horizontal and oblique asymptotes for #(x+4)/(3x^2+5x-2)#?

##### 1 Answer

Apr 18, 2016

vertical asymptotes x = -2 , x

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 :

# 3x^2 + 5x - 2 = 0 → (3x-1)(x+2) = 0 #

#rArr x = - 2 , x = 1/3" are the asymptotes "# Horizontal asymptotes occur as

#lim_(xto+-oo) f(x) to 0 # When the degree of the numerator < degree of the denominator , the equation is always

y = 0.Oblique asymptotes occur when the degree of the numerator > degree of the denominator . This is not the case here hence there are no oblique asymptotes.

graph{(x+4)/(3x^2+5x-2) [-10, 10, -5, 5]}