AP Calculus AB and BC glossary
Vertical asymptote
A vertical asymptote is a vertical line that a graph approaches without ever reaching, occurring wherever at least one one-sided limit is infinite. For a rational function, these sit at the zeros of the denominator that remain after all common factors cancel.
The order matters: factor the numerator and denominator, cancel common factors first, and only then set the remaining denominator to zero. A factor that cancels produces a hole rather than an asymptote.
A graph may cross a horizontal asymptote but can never cross a vertical one, because a vertical asymptote sits at an input where the function has no value at all.
Appears in: Unit 1: Limits and Continuity