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Study Guides > College Algebra CoRequisite Course

Introduction to Graphs of Polynomial Functions

Learning Outcomes

By the end of this lesson, you will be able to:
  • Identify zeros of polynomial functions with even and odd multiplicity.
  • Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the Intermediate Value Theorem.
  • Write the equation of a polynomial function given its graph.
The revenue in millions of dollars for a fictional cable company from 2006 through 2013 is shown in the table below.
Year 2006 2007 2008 2009 2010 2011 2012 2013
Revenue 52.4 52.8 51.2 49.5 48.6 48.6 48.7 47.1
The revenue can be modeled by the polynomial function

R(t)=−0.037t4+1.414t3−19.777t2+118.696t−205.332R\left(t\right)=-0.037{t}^{4}+1.414{t}^{3}-19.777{t}^{2}+118.696t - 205.332

where R represents the revenue in millions of dollars and t represents the year, with t = 6 corresponding to 2006. Over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing? 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.

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