An asymptote is a line or curve that approaches a given curve arbitrarily closely.

An asymptote is a line or curve that approaches a given curve arbitrarily closely, as illustrated in the above diagram. The plot above shows 1/x, which has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

asymptosy | asymptotic | asymptotic curve | limit

high school level (AP calculus AB, California Algebra II standard)