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

##### 1 Answer

Jun 8, 2016

vertical asymptotes x = ± 1

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^2-1=0rArrx^2=1rArrx=±1" are the asymptotes"# Horizontal asymptotes occur as

#lim_(xto+-oo),f(x)toc" (a constant)"# divide terms on numerator/denominator by

#x^2#

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

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

#rArry=3" is the asymptote"#

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