Question

How do you find the asymptotes for `(2x-4)/(x^2-4)`?

Answer 1

vertical asymptote x = -2
horizontal asymptote y = 0

Explanation:

The first step is to factorise and simplify the function

`rArr(2 cancel((x-2)))/(cancel((x-2)) (x+2))=2/(x+2`

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation set the denominator equal to zero.

solve: x + 2 = 0 → x = -2 is the asymptote

Horizontal asymptotes occur as `lim_(xto+-oo) , f(x) to 0`

divide terms on numerator/denominator by x

`rArr (2/x)/(x/x+2/x)=(2/x)/(1+2/x)`

as `xto+-oo, y to 0/(1+0)`

`rArry=0" is the asymptote"`
graph{2/(x+2) [-10, 10, -5, 5]}