Algebra and Trigonometry, 5th Edition

4.5 Rational Functions

• For a rational function, find the domain and graph the function, identifying all of the asymptotes.

• Solve applied problems involving rational functions.

Now we turn our attention to functions that represent the quotient of two polynomials. Whereas the sum, the difference, or the product of two polynomials is a polynomial, in general the quotient of two polynomials is not itself a polynomial.

A rational number can be expressed as the quotient of two integers, $p/q$, where $q\ne 0$. A rational function is formed by the quotient of two polynomials, $p(x)/q(x)$, where $q(x)\ne 0$. Here are some examples of rational functions and their graphs.

Rational Function

A rational function is a function f that is a quotient of two polynomials. ...