Asymptotes

An asymptote is a line that a graph approaches but never touches. It can be horizontal, vertical, or oblique.

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

A vertical asymptote is a vertical line that the graph of a function approaches as the function's value approaches infinity or negative infinity.

To find horizontal asymptotes of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, the asymptote is y=ratio of leading coefficients.

Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is not zero.

The vertical asymptote is x = 3.

The function has 2 vertical asymptotes at x = 3 and x = -3.

At a vertical asymptote, the graph of the function approaches infinity or negative infinity.