Introduction to Power Functions and Polynomial Functions


By the end of this lesson, you will be able to:

  • Identify power functions.
  • Identify end behavior of power functions.
  • Identify polynomial functions.
  • Identify the degree and leading coefficient of polynomial functions.
Three birds on a cliff with the sun rising in the background.

Figure 1. (credit: Jason Bay, Flickr)

Suppose a certain species of bird thrives on a small island. Its population over the last few years is shown below.

Year 2009 2010 2011 2012 2013
Bird Population 800 897 992 1,083 1,169

The population can be estimated using the function [latex]P\left(t\right)=-0.3{t}^{3}+97t+800,\\[/latex] where [latex]P\left(t\right)\\[/latex] represents the bird population on the island t years after 2009. 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.