Remember that an asymptote is a line that the graph of a function approaches but never touches. Rational functions contain asymptotes, as seen in this example:In this example, there is a vertical asymptote at x = 3 and a horizontal asymptote at y = 1. The curves approach these asymptotes ...
Vertical and horizontal asymptotes can occur in a variety of different types of functions. However, slant asymptotes most commonly appear for two types of functions. The first type of function is a rational function, of the form {eq}\frac{f(x)}{g(x)} {/eq}, where {eq}f(x) {/eq}...