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

1 Answer
Jun 8, 2016

Answer:

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]}