Determine
the vertical and horizontal asymptotes of f(x)=8x^{2}/(x^{2}-1).

Horizontal asymptote at y=

Vertical asymptotes at x= and x= (order from left to right)

The graph of f has one horizontal asymptote because the degrees of the leading

variables
of the numerator and denominator are the same (both have x^{2}_{ }as
biggest degree);

Since the degrees are the same, the graph of f has the line y=8/1 (the ratio of the leading coefficients) as a horizontal asymptote.

y=8 : horizontal asymptote

The graph of f has vertical asymptotes at the zeros of the denominator (D(x)).

The zeros
of D(x)=x^{2}-1=(x+1)(x-1) are at x=-1 and x=1.

x=-1 and x=1 : vertical asymptotes