How to find the asymptotes for (3x^2) / (x^2-4)?

1 Answer
Aug 11, 2018

(3x^2)/(x^2-4) has horizontal asymptote y=3 and vertical asymptotes x=-2 and x=2

Explanation:

Note that:

lim_(x->+-oo) (3x^2)/(x^2-4) = lim_(x->+-oo) 3/(1-4/x^2) = 3

So y=3 is a horizontal asymptote.

Also:

x^2-4 = (x-2)(x+2)

So the denominator is zero when x=+-2 and the numerator is non-zero at those values.

So (3x^2)/(x^2-4) has vertical asymptotes at x=-2 and x=2

graph{(y-(3x^2)/(x^2-4)) = 0 [-10.09, 9.91, -3.6, 6.4]}