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.
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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.