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/ |
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