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.

y 2005 2006 2007 2008 2009 2010 2011 2012
C(y) 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. ↵