## Introduction to Rates of Change and Behaviors of Graphs

### LEARNING OBJECTIVES

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

• Find the average rate of change of a function.
• Use a graph to determine where a function is increasing, decreasing, or constant.
• Use a graph to locate local maxima and local minima.
• Use a graph to locate the absolute maximum and absolute minimum.

Gasoline costs have experienced some wild fluctuations over the last several decades. The table below[1] lists the average cost, in dollars, of a gallon of gasoline for the years 2005–2012. The cost of gasoline can be considered as a function of year.

 $y$ 2005 2006 2007 2008 2009 2010 2011 2012 $C\left(y\right)$ 2.31 2.62 2.84 3.3 2.41 2.84 3.58 3.68

If we were interested only in how the gasoline prices changed between 2005 and 2012, we could compute that the cost per gallon had increased from $2.31 to$3.68, an increase of \$1.37. While this is interesting, it might be more useful to look at how much the price changed per year. In this section, we will investigate changes such as these.