AP Calculus AB and BC glossary
Horizontal asymptote
A horizontal asymptote is a horizontal line that a graph approaches as the input grows without bound in either direction. A function has one exactly when its limit at infinity or at negative infinity is a finite number.
Because it is defined by a limit at infinity, a function can have at most two horizontal asymptotes, one in each direction. Rational functions have the same one on both sides, but and functions built from often differ.
Crossing is allowed
Nothing stops a graph from crossing its horizontal asymptote, even many times. The asymptote describes only the long-run behavior, not a barrier.
Appears in: Unit 1: Limits and Continuity