Question

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

Answer 1

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]}