3.2 - Polynomial Functions of Higher Degree

3.2 - Polynomial Functions of Higher Degree -

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<?xml version="1.0" encoding="iso-8859-1"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>3.2 - Polynomial Functions of Higher Degree</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> <style type="text/css"> <!-- .bigletter { font-size: large; color: #FF0000; } --> </style> </head> <body> <h1>3.2 - Polynomial Functions of Higher Degree</h1> <h2>Graphs of Polynomials</h2> <p>Polynomials are continuous and smooth everywhere. </p> <ul> <li>A continuous function means that it can be drawn <strong>without picking up your pencil</strong>. There are no jumps or holes in the graph of a polynomial function. </li> <li>A smooth curve means that there are <strong>no sharp turns</strong> (like an absolute value) in the graph of the function.</li> <li>The <strong>y-intercept</strong> of the polynomial is <strong>the constant</strong> term a<sub>0</sub>.</li> </ul> <h3>Leading Coefficient Test (right hand behavior)</h3> <ul> <li>If the leading coefficient, a<sub>n</sub>, of the polynomial is <strong>positive</strong>, then the right hand side of the graph will <strong>rise</strong> towards + infinity. </li> <li>If the leading coefficient, a<sub>n</sub>, of the polynomial is <strong>negative</strong>, then the right hand side of the graph will <strong>fall</strong> towards - infinity.</li> </ul> <h3>Degree of the Polynomial (left hand behavior)</h3> <ul> <li>If the degree, n, of the polynomial is <strong>even</strong>, the left hand side will do the <strong>same</strong> as the right hand side.</li> <li>If the degree, n, of the polynomial is <strong>odd</strong>, the left hand side will do the <strong>opposite</strong> of the right hand side.</li> </ul> <p>Get used to this even-same, odd-changes notion. We will be seeing it a lot
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This note was uploaded on 10/18/2011 for the course MAT 1033 taught by Professor Brown during the Spring '10 term at Valencia.

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3.2 - Polynomial Functions of Higher Degree -

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