An asymptote is a line that a graph approaches but never touches. There are two types of asymptotes: horizontal asymptotes, which are horizontal lines a graph approaches, and vertical asymptotes, which are vertical lines a graph approaches. As a graph gets closer to an asymptote, the space between the graph and asymptote decreases infinitely. Vertical asymptotes occur when factors in the denominator equal zero and do not cancel out factors in the numerator.