Asymptote

When a straight line approaches a curve that even if infinitely extended would never meet it, either can be described as an asymptote. (Think of standing a foot away from something: Every second you take a step that is half the distance between you and that object; your steps get smaller and smaller, and you get closer and closer to it but never actually get there.)

A specific example of asymptotes can be found in the graph of the function y = x^-1, in which there are two asymptotes; the curve approaches the line y = 0 but never reaches it, and it approaches the line x = 0 but never reaches it.

Asymptotes do not need to be parallel to the x- and y-axes, as shown by the graph of x+x^-1, which is asymptotic to both the y-axis and y=x.

A function f(x) can be said to be asymptotic to a function g(x) as x->&inf;. This has any of four distinct meanings: 1. f(x)-g(x)->0. 2. f(x)/g(x)->1. 3. f(x)/g(x) has a nonzero limit. 4. f(x)/g(x) is bounded and does not approach zero. See Big O notation.