4: Polynomial and Rational Functions
- Page ID
- 191366
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- 4.1: 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.
- 4.2: 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.
- 4.3: Dividing Polynomials
- Just as we use division in arithmetic to find factors of a whole number. Polynomial division can be used to factor polynomials. In this section we will learn the Division Algorithm for polynomials using both Long and Synthetic division processes.
- 4.4: Zeros of Polynomial Functions
- In the last section, we learned how to divide polynomials. We can now use polynomial division to evaluate polynomials using the Remainder Theorem. If the polynomial is divided by x–c, the remainder may be found quickly by evaluating the polynomial function at x=c, that is, f(c). When f(c)=0, we call the value c a "zero" of the polynomial.
- 4.5: 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.
Contributors
Jay Abramson (Arizona State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/precalculus.