A *rational function* is any function that is a ratio of two polynomials. That is, a rational function is of the form , where and are both polynomials and .
Here are some examples of rational functions:
All polynomial functions are technically rational functions, since any polynomial can be written as , and is a polynomial of order zero.

A *vertical asymptote* is a vertical line that a curve will approach but never touch. On either side of this line, then, the curve will to grow toward or toward . The function has two vertical asymptotes, and , as you can see in the graph below.

A more formal definition of a vertical asymptote might sound something like this: The line *vertical asymptpte* of the graph of a function if, as from the right or from the left, or .

A *horizontal asymptote* is a horizontal line that a curve approaches either as gets bigger and bigger, approaching , or as gets smaller and smaller, approaching . Many rational functions have horizontal asymptotes. Whereas curves may not cross their vertical asymptotes, they may cross their horizontal asymptotes at values of that are relatively close to . The graph of shows us how what this could look like:

A more formal definition of a horizontal asymptote might sound something like this: The line is a *horizontal asymptote* of the graph of the function if, as or , .