Question

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

Answer 1

vertical asymptotes at x = ± 2
horizontal asymptote at y = 0

Explanation:

vertical asymptotes occur as the denominator of a rational function approaches zero. To find the equation let the denominator equal zero.

solve : `x^2 - 4 = 0`

this is a difference of squares and factors as follows:

# x^2 - 4 = (x+2)(x-2) = 0 → x = ± 2 , the equations of the asymptotes

horizontal asymptotes occur as `lim_(x→±∞) f(x) → 0`

If the degree of the numerator < degree of denominator then the equation of the asymptote is y = 0
graph{1/(x^2-4) [-10, 10, -5, 5]}