4.2 - Logarithmic Functions and Their Graphs

4.2 - Logarithmic Functions and Their Graphs -

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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>4.2 - Logarithmic Functions and Their Graphs</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> </head> <body> <h1>4.2 - Logarithmic Functions and Their Graphs</h1> <h2>Inverse of Exponential Functions</h2> <p><img src="log2.gif" alt="y=log2(x)" width="305" height="298" class="imgrt" />We stated in the section on <a href="exponential.html">exponential functions</a>, that exponential functions were one-to-one. One-to-one functions had the special property that they have inverses that are also functions. And, as many of you said in class, and I'm so glad you remember, one-to-one functions can be applied to both sides of an equation. They also pass a horizontal line test. </p> <p>This section is about the inverse of the exponential function. The inverse of an exponential function is a logarithmic function. Remember that the inverse of a function is obtained by switching the x and y coordinates. This reflects the graph about the line y=x. As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve.</p> <p>The table below demonstrates how the x and y values of the points on the expontential curve can be switched to find the coordinates of the points on the logarithmic curve.</p> <table border="1" cellspacing="0" cellpadding="3"> <tr> <th class="datahdr" scope="col">Point on <br /> exponential curve</th> <th class="datahrl" scope="col">Corresponding point <br /> on logarithmic curve</th> </tr> <tr> <td class="datar">(-3, 1/8)</td> <td class="datal">(1/8, -3)</td> </tr> <tr> <td class="datar">(-2, 1/4)</td> <td class="datal">(1/4, -2)</td> </tr> <tr> <td class="datar">(-1, 1/2)</td> <td class="datal">(1/2, -1)</td> </tr> <tr> <td class="datar">(0, 1)</td> <td class="datal">(1, 0)</td> </tr> <tr>
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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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4.2 - Logarithmic Functions and Their Graphs -

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