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MathGroup Archive 2002

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Re: Definitions of the functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34975] Re: [mg34963] Definitions of the functions
  • From: BobHanlon at aol.com
  • Date: Mon, 17 Jun 2002 03:26:50 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 6/16/02 12:29:53 AM, pmg at wp.pl writes:

>How do I define a function that is described by different formulas depending
>of the interval which the argument is given in????
>For example:
>
>y=x             for  -inf<x<-5
>y=x*x          for  -5<=x<18
>y=sin x        for all the remaining values of x.
>

method 1

Clear[y];
y[x_/;x<-5] := x ;
y[x_/;x<18] := x^2;
y[x_] := Sin[x];

method 2

Clear[y];
y[x_] := x + UnitStep[x+5]*(x^2-x) +
 
      UnitStep[x-18]*(Sin[x]-x^2);

method 3

Clear[y];
y[x_] := Which[
      x < -5, x,
 
     x < 18, x^2,
      True, Sin[x]];

method 4

Clear[y];
y[x_] := If[x<-5, x, If[x<18, x^2, Sin[x]]];


Bob Hanlon
Chantilly, VA  USA


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