{"id":133,"date":"2023-06-21T13:22:36","date_gmt":"2023-06-21T13:22:36","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/introduction-rates-of-change-and-behavior-of-graphs\/"},"modified":"2024-01-08T19:01:14","modified_gmt":"2024-01-08T19:01:14","slug":"introduction-rates-of-change-and-behavior-of-graphs","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/introduction-rates-of-change-and-behavior-of-graphs\/","title":{"raw":"2.4 Introduction to Rates of Change and Behaviors of Graphs","rendered":"2.4 Introduction to Rates of Change and Behaviors of Graphs"},"content":{"raw":"

What you\u2019ll learn to do: Find rates of change of a function and identify behaviors of various graphs<\/h2>\r\nGasoline costs have experienced some wild fluctuations over the last several decades. The table below[footnote]http:\/\/www.eia.gov\/totalenergy\/data\/annual\/showtext.cfm?t=ptb0524. Accessed 3\/5\/2014.[\/footnote]\u00a0lists the average cost, in dollars, of a gallon of gasoline for the years 2005\u20132012. The cost of gasoline can be considered as a function of year.\r\n\r\n\r\n\r\n\r\n
[latex]y[\/latex]<\/strong><\/td>\r\n2005<\/td>\r\n2006<\/td>\r\n2007<\/td>\r\n2008<\/td>\r\n2009<\/td>\r\n2010<\/td>\r\n2011<\/td>\r\n2012<\/td>\r\n<\/tr>\r\n
[latex]C\\left(y\\right)[\/latex]<\/strong><\/td>\r\n2.31<\/td>\r\n2.62<\/td>\r\n2.84<\/td>\r\n3.30<\/td>\r\n2.41<\/td>\r\n2.84<\/td>\r\n3.58<\/td>\r\n3.68<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIf 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<\/em>. In this section, we will investigate changes such as these.","rendered":"

What you\u2019ll learn to do: Find rates of change of a function and identify behaviors of various graphs<\/h2>\n

Gasoline costs have experienced some wild fluctuations over the last several decades. The table below[1]<\/sup><\/a>\u00a0lists the average cost, in dollars, of a gallon of gasoline for the years 2005\u20132012. The cost of gasoline can be considered as a function of year.<\/p>\n\n\n\n\n
[latex]y[\/latex]<\/strong><\/td>\n2005<\/td>\n2006<\/td>\n2007<\/td>\n2008<\/td>\n2009<\/td>\n2010<\/td>\n2011<\/td>\n2012<\/td>\n<\/tr>\n
[latex]C\\left(y\\right)[\/latex]<\/strong><\/td>\n2.31<\/td>\n2.62<\/td>\n2.84<\/td>\n3.30<\/td>\n2.41<\/td>\n2.84<\/td>\n3.58<\/td>\n3.68<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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<\/em>. In this section, we will investigate changes such as these.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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