1.5 - Shifting, Reflecting, and Stretching Graphs

# 1.5 - Shifting, Reflecting, and Stretching Graphs -

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<?xml version="1.0" encoding="utf-8"?> <!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>1.5 - Shifting, Reflecting, and Stretching Graphs</title> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> </head> <body> <h1>1.5 - Shifting, Reflecting, and Stretching Graphs</h1> <h2>Definitions</h2> <dl> <dt>Abscissa</dt> <dd>The x-coordinate</dd> <dt>Ordinate</dt> <dd>The y-coordinate</dd> <dt>Shift</dt> <dd>A translation in which the size and shape of a graph of a function is not changed, but the location of the graph is.</dd> <dt>Scale</dt> <dd>A translation in which the size and shape of the graph of a function is changed.</dd> <dt>Reflection</dt> <dd>A translation in which the graph of a function is mirrored about an axis.</ dd> </dl> <h2>Common Functions</h2> <p>Part of the beauty of mathematics is that almost everything builds upon something else, and if you can understand the foundations, then you can apply new elements to old. It is this ability which makes comprehension of mathematics possible. If you were to memorize every piece of mathematics presented to you without making the connection to other parts, you will 1) become frustrated at math and 2) not really understand math. </p> <p>There are some basic graphs that we have seen before. By applying translations to these basic graphs, we are able to obtain new graphs that still have all the properties of the old ones. By understanding the basic graphs and the way translations apply to them, we will recognize each new graph as a small variation in an old one, not as a completely different graph that we have never seen before. Understanding these translations will allow us to quickly recognize and sketch a new function without having to resort to plotting points. </p> <p>These are the common functions you should know the graphs of at this time: </p> <ul> <li>Constant Function: y = c</li> <li>Linear Function: y = x</li> <li>Quadratic Function: y = x<sup>2</sup></li> <li>Cubic Function: y = x<sup>3</sup></li>

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<li>Absolute Value Function: y = |x|</li> <li>Square Root Function: y = sqrt(x)</li> <li><a href="graphs.html">Greatest Integer Function</a>: y = int(x) was talked about in the last section.</li> </ul> <table border="1" cellspacing="0" cellpadding="3"> <tr> <td><p>Constant Function</p> <p><img src="constant.gif" alt="Constant function" width="278" height="271" / ></p></td> <td><p>Linear Function</p> <p><img src="linear.gif" alt="Linear function" width="278" height="271" /></p></td> <td><p>Quadratic Function</p> <p><img src="quadratic.gif" alt="Quadratic function" width="278" height="271" /></p></td> </tr> <tr> <td><p>Cubic function</p> <p><img src="cubic.gif" alt="Cubic function" width="278" height="271" /></p></td> <td><p>Absolute Value function</p> <p><img src="abs.gif" alt="Absolute Value function" width="278"
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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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1.5 - Shifting, Reflecting, and Stretching Graphs -

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