A graph of hyperbola in (blue) and its conjugate (in green), as well as its asymptotes, in red.

An asymptote is a line on a graph of a curve which the curve is always approaching as it tends towards infinity. Horizontal or vertical asymptotes are commonly used in mathematics, however, an asymptote can be positioned at any angle. An example of a graph with asymptotes is

f(x) = \frac{1}{x}

which has a horizontal asymptote at y=0 and a vertical asymptote at x=0.

Asymptotes can be found by graphing or with calculus, as the limit at the point of a vertical asymptote from a given side will be either positive or negative infinity, and the limit of positive or negative infinity will give the horizontal asymptote.