Purpose of Absolute Value and Piecewise FunctionsDate: 12/09/2001 at 00:12:05 From: Kyle Hill Subject: Purpose for Absolute Value Functions and Piecewise Functions This is more of a word question than a mathematical question... What is the purpose of absolute value and of piecewise functions? I can't really think of a good reason to do them. Thanks a lot. -Kyle Hill Date: 12/09/2001 at 23:03:09 From: Doctor Peterson Subject: Re: Purpose for Absolute Value Functions and Piecewise Functions Hi, Kyle. A good case could be made to say that piecewise-defined functions are more realistic than ordinary smooth functions, so it's good to get used to working this way. There are many real-life problems in which something changes in different regions; for example, if you were considering the effect of gravity at different distances from the center of the earth, the fact that there is rock up to a certain distance, then air, then "empty" space means that you will need at least two regions with different formulas for gravitational acceleration. As in this example, the real world is not uniform, but has boundaries and sudden changes everywhere! I searched our archives for applications of absolute value, to see what other ideas we can give. Here are two pages listing a few: Practical Applications of Absolute Value http://mathforum.org/library/drmath/view/57177.html Absolute Value http://mathforum.org/library/drmath/view/53087.html This problem I helped with requires an absolute value to get it right: Find the Path and the Time Taken http://mathforum.org/library/drmath/view/53778.html In this case, the absolute value arises in its most basic form: the distance between two points. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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