asymptote

A line a graph approaches but (usually) never crosses near a bad point or at infinity.

An asymptote is a line that a graph gets arbitrarily close to without (typically) touching it. A vertical asymptote occurs where a rational function's denominator hits zero and the numerator doesn't; horizontal and slant asymptotes describe the graph's behavior as $x \to \pm\infty$ .

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Examples

$f(x) = \frac{1}{x-2}$ has a vertical asymptote at $x=2$ and a horizontal asymptote at $y=0$ .