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### Purpose of Absolute Value and Piecewise Functions

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Date: 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/
```
Associated Topics:
High School Functions

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