# 5: Polynomial and Rational Functions


In this section, we will investigate quadratic functions, which frequently model problems involving area and projectile motion. Working with quadratic functions can be less complex than working with higher degree functions, so they provide a good opportunity for a detailed study of function behavior.
• 5.2: Power Functions and Polynomial Functions
Suppose a certain species of bird thrives on a small island. The population can be estimated using a polynomial function. We can use this model to estimate the maximum bird population and when it will occur. We can also use this model to predict when the bird population will disappear from the island. In this section, we will examine functions that we can use to estimate and predict these types of changes.
• 5.3: Graphs of Polynomial Functions
The revenue in millions of dollars for a fictional cable company can be modeled by the polynomial function From the model one may be interested in which intervals the revenue for the company increase or decreases? These questions, along with many others, can be answered by examining the graph of the polynomial function. We have already explored the local behavior of quadratics, a special case of polynomials. In this section we will explore the local behavior of polynomials in general.
• 5.4: Rational Functions
In the last few sections, we have worked with polynomial functions, which are functions with non-negative integers for exponents. In this section, we explore rational functions, which have variables in the denominator.

Thumbnail: Identifying the behavior of the graph at an x-intercept by examining the multiplicity of the zero.

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