Introduction to Behaviors of Graphs

LEARNING OBJECTIVES

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

  • 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

From this table, we see that the cost per gallon increased between 2005 and 2008 from $2.31 to $3.30, decreased between 2008 and 2009 from $3.30 to $2.41, and increased again between 2010 and 2012 from $2.84 to $3.68. In these section, we will investigate changes such as these.

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