2.3polynomialfns - Section 2.3 Polynomial Functions and...

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Section 2.3 Polynomial Functions and Their Graphs
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Smooth, Continuous Graphs
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Polynomial functions of degree 2 or higher have graphs that are smooth and continuous. By smooth , we mean that the graphs contain only rounded curves with no sharp corners. By continuous , we mean that the graphs have no breaks and can be drawn without lifting your pencil from the rectangular coordinate system.
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Notice the breaks and lack of smooth curves.
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End Behavior of Polynomial Functions
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Odd-degree polynomial functions have graphs with opposite behavior at each end. Even-degree polynomial functions have graphs with the same behavior at each end.
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Example Use the Leading Coefficient Test to determine the end behavior of the graph of f(x)= - 3x 3 - 4x + 7
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Example Use the Leading Coefficient Test to determine the end behavior of the graph of f(x)= - .08x 4 - 9x 3 +7x 2 +4x + 7 This is the graph that you get with the standard viewing window. How do you know that you need to change the window to see the end behavior of the function? What viewing window will allow you to see the end behavior?
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Zeros of Polynomial Functions
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  • Fall '06
  • Moffett
  • Continuous function, polynomial function, OPPO, x3+2x2- 4x-8=0

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