A specific example of asymptotes can be found in the graph of the function f(x) = 1 / x, in which two asymptotes are being approached: the line y = 0 and the line x = 0. The curve approaches them, but, never reaches them. A curve approaching a vertical asymptote (such as in the preceding example's y = 0, which has an undefined slope) could be said to approach an "infinite limit", although infinity is not technically considered a limit. A curve approaching a horizontal asymptote (such as in the preceding example's x = 0, which has a slope of 0) does approach a "true limit".
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 the line y = x. When an asymptote is not parallel to the x or y axes, it is called an oblique asymptote.
A function f(x) can be said to be asymptotic to a function g(x) as x->∞. This has any of four distinct meanings: