An asymptote is a line or curve that approaches a given curve arbitrarily closely, as illustrated in the above diagram.
The plot above shows 
,
which has a vertical asymptote at 
and a horizontal asymptote at 
.
Asymptote
See also
Asymptosy, Asymptotic, Asymptotic Curve, Limit Explore this topic in the MathWorld classroomExplore with Wolfram|Alpha
References
Giblin, P. J. "What is an Asymptote?" Math. Gaz. 56, 274-284, 1972.Referenced on Wolfram|Alpha
AsymptoteCite this as:
Weisstein, Eric W. "Asymptote." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Asymptote.html