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/