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

##### 1 Answer

May 31, 2016

vertical asymptotes x = ± 2

horizontal asymptote y = 3

#### 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 :

#x^2-4=0rArr(x-2)(x+2)=0rArrx=±2#

#rArrx=-2,x=2" are the asymptotes"# Horizontal asymptotes occur as

#lim_(xto+-oo),g(x)to0# divide terms on numerator/denominator by

#x^2#

#((3x^2)/x^2+(2x)/x^2-1/x^2)/(x^2/x^2-4/x^2)=(3+2/x-1/x^2)/(1-4/x^2)# as

#xto+-oo,g(x)to(3+0-0)/(1-0)#

#rArry=3" is the asymptote"#

graph{(3x^2+2x-1)/(x^2-4) [-10, 10, -5, 5]}