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 towardor 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 lineis a 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
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 , .