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.

[latex]y[/latex] 2005 2006 2007 2008 2009 2010 2011 2012
[latex]C\left(y\right)[/latex] 2.31 2.62 2.84 3.30 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.

  1. http://www.eia.gov/totalenergy/data/annual/showtext.cfm?t=ptb0524. Accessed 3/5/2014. ↵