Asymptotes

Definition

Asymptotes are lines that a curve approaches but never touches. They can be horizontal, vertical, or slanted and help describe the behavior of a function as it approaches infinity or negative infinity.

Related terms

Vertical Asymptote: A vertical asymptote is a line that a graph approaches as x-values get infinitely large or small. It indicates values where the function becomes undefined.

Horizontal Asymptote: A horizontal asymptote is a line that a graph approaches as x-values get infinitely large or small. It describes long-term behavior and limits of the function.

Slant Asymptote (Oblique Asymptote): A slant asymptote occurs when there is no horizontal or vertical asymptote, but instead, the curve approaches a diagonal line at infinity.