Question

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

Answer 1

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]}