How do you find the asymptotes for f(x)=(3x^2+2) / (x^2 -1)f(x)=3x2+2x21?

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"x21=0x2=1x=±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]}