An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.

How are asymptotes found?

The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator. Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0. Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.

Are asymptotes calculus?

Asymptotes are useful guides to complete the graph of a function. An asymptote is a line to which the curve of the function approaches at infinity or at certain points of discontinuity. There are three types of asymptotes: vertical asymptotes, horizontal asymptotes and oblique asymptotes.