asymptote

A line a curve gets closer and closer to without ever quite touching it.

An asymptote is a straight line that a function's graph approaches arbitrarily closely, without ever crossing or reaching it in the limit — a vertical asymptote as the input heads toward some fixed value, a horizontal asymptote as the input grows without bound in either direction.

Examples

$f(x)=1/x$ shoots toward $\pm\infty$ near $x=0$ (a vertical asymptote) and flattens toward $y=0$ far from the origin (a horizontal asymptote).