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1.4 - Graphs of Functions

# 1.4 - Graphs of Functions -

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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>1.4 - Graphs of Functions</title> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> </head> <body> <h1>1.4 - Graphs of Functions</h1> <h2>Definitions</h2> <p>These definitions are mathematically loose (that means a mathematician would pull his or her hair out but a normal person might understand them).</p> <dl> <dt><strong>Graph of a function</strong></dt> <dd>The graph of a function f is the set of all ordered pairs ( x, f(x) ) where x is in the domain of f.</dd> <dt><strong>Increasing Function</strong></dt> <dd>A function is increasing on an open interval if the function rises (positive slope) on the interval as you move from left to right.</dd> <dt><strong>Decreasing Function</strong></dt> <dd>A function is decreasing on an open interval if the function falls (negative slope) on the interval as you move from left to right.</dd> <dt><strong>Constant Function</strong></dt> <dd>A function is constant on an open interval if the function remains constant (horizontal line segment) on the interval as you move from left to right.</dd> <dt><strong>Relative Minimum</strong></dt> <dd>A function has a relative minimum at x=a if the function evaluated at x=a is less than at any other point in the neighborhood surrounding x=a. A <em>relative</em> minimum is the lowest point in an open interval, but not necessarily over the entire domain. Relative

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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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1.4 - Graphs of Functions -

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