# 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.

Get *Algebra and Trigonometry, 5th Edition* now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.