Associated Topics || Dr. Math Home || Search Dr. Math

### Which Piece of a Piecewise Function?

```Date: 09/05/2003 at 00:03:58
From: Theresa
Subject: piecewise functions

When a function is defined piecewise with two or more definitions how
do you know which definition to use to calculate a function value?
```

```
Date: 09/05/2003 at 12:42:01
From: Doctor Peterson
Subject: Re: piecewise functions

Hi, Theresa.

The quick answer: just pick the right piece!

Here's what I mean. A piecewise-defined function is defined by
breaking up the x axis into pieces (say, x<-2, -2<=x<=2, and x>2) and
defining it on each. If you want to find the value at, say, x=3, you
just see which piece that fits into; since 3>2, it is in the third
piece, and you use the corresponding definition.

The definition really tells you just what to do, once you are used to
reading it. It may look like this:

f(x) = 2x+7   for x < -2

3      for -2 <= x <= 2

7-2x   for x > 2

Then

f(3) = 7 - 2*3 = 1  since 3 > 2 and we use the third part.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Functions

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search