{"id":213,"date":"2023-06-21T13:22:44","date_gmt":"2023-06-21T13:22:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/introduction-graphs-of-polynomial-functions\/"},"modified":"2024-01-08T19:12:51","modified_gmt":"2024-01-08T19:12:51","slug":"introduction-graphs-of-polynomial-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/introduction-graphs-of-polynomial-functions\/","title":{"raw":"4.2 Introduction to Graphs of Polynomial Functions","rendered":"4.2 Introduction to Graphs of Polynomial Functions"},"content":{"raw":"

What you\u2019ll learn to do: Create graphs and write equations for polynomial functions<\/h2>\r\nThe revenue in millions of dollars for a fictional cable company from 2006 through 2013 is shown in the table below.<\/b>\r\n\r\n\r\n\r\n\r\n
Year<\/strong><\/td>\r\n2006<\/td>\r\n2007<\/td>\r\n2008<\/td>\r\n2009<\/td>\r\n2010<\/td>\r\n2011<\/td>\r\n2012<\/td>\r\n2013<\/td>\r\n<\/tr>\r\n
Revenue<\/strong><\/td>\r\n52.4<\/td>\r\n52.8<\/td>\r\n51.2<\/td>\r\n49.5<\/td>\r\n48.6<\/td>\r\n48.6<\/td>\r\n48.7<\/td>\r\n47.1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe revenue can be modeled by the polynomial function\r\n

[latex]R\\left(t\\right)=-0.037{t}^{4}+1.414{t}^{3}-19.777{t}^{2}+118.696t - 205.332[\/latex]<\/p>\r\nwhere R<\/em>\u00a0represents the revenue in millions of dollars and t<\/em>\u00a0represents the year, with t<\/em> = 6\u00a0corresponding to 2006. Over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing? These questions, along with many others, can be answered by examining the graph of the polynomial function. We have already explored the local behavior of quadratics, a special case of polynomials. In this section we will explore the local behavior of polynomials in general.","rendered":"

What you\u2019ll learn to do: Create graphs and write equations for polynomial functions<\/h2>\n

The revenue in millions of dollars for a fictional cable company from 2006 through 2013 is shown in the table below.<\/b><\/p>\n\n\n\n\n
Year<\/strong><\/td>\n2006<\/td>\n2007<\/td>\n2008<\/td>\n2009<\/td>\n2010<\/td>\n2011<\/td>\n2012<\/td>\n2013<\/td>\n<\/tr>\n
Revenue<\/strong><\/td>\n52.4<\/td>\n52.8<\/td>\n51.2<\/td>\n49.5<\/td>\n48.6<\/td>\n48.6<\/td>\n48.7<\/td>\n47.1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The revenue can be modeled by the polynomial function<\/p>\n

[latex]R\\left(t\\right)=-0.037{t}^{4}+1.414{t}^{3}-19.777{t}^{2}+118.696t - 205.332[\/latex]<\/p>\n

where R<\/em>\u00a0represents the revenue in millions of dollars and t<\/em>\u00a0represents the year, with t<\/em> = 6\u00a0corresponding to 2006. Over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing? These questions, along with many others, can be answered by examining the graph of the polynomial function. We have already explored the local behavior of quadratics, a special case of polynomials. In this section we will explore the local behavior of polynomials in general.<\/p>\n\n\t\t\t

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