What are the vertical and horizontal asymptotes of the function f (x) = 3x^2/x^2-4

The horizontal asymptote in this case, because the degree of the numerator is the same as the degree of the denominator, is equal to the fraction created by the leading coefficients: 3/1 which is 3.  The vertical asymptotes are found when the denominator of the function is set equal to 0 and then solved for x. The denominator factors to (x + 2)(x - 2) so the vertical asymptotes exist at x = 2 and x = -2.