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MathGroup Archive 2004

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Re: Piecewise functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51568] Re: [mg51553] Piecewise functions
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sat, 23 Oct 2004 00:21:50 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

Clear[y];
y[x_ /; x>3]:= x;
y[x_ /; -1<x<3]:= -x;
y[x_] := 1;

Plot[y[x],{x,-3,5}];

However, with this definition you cannot directly plot the derivative.

Plot[y'[x],{x,-3,5}];

Whereas, using UnitStep

Clear[y];
y[x_] := 1-UnitStep[x+1]*(x+1)+
      UnitStep[x-3]*2x;

Plot[y[x],{x,-3,5}];

Plot[y'[x],{x,-3,5},PlotRange->All];


Bob Hanlon

> 
> From: Luca <luca at nospam.it>
To: mathgroup at smc.vnet.net
> Date: 2004/10/21 Thu PM 10:22:10 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg51568] [mg51553] Piecewise functions
> 
> Hi all. I'm studying for the exam of signals and systems and I was
> trying to plot some kind of functions I transformed for exercise. So, I
> need to plot piecewise functions like:
> 
> y(x) = x if x > 3
> y(x) = -x if -1 < x < 3
> y(x) = 1 else
> 
> (should have been a system).
> I found out in the guide the chapter about this, and I learned that it
> is possible with the function UnitStep, which I know. Anyway, I found
> it difficult to determine the equation of the function using this
> method. Is it possible to do it simply writing everything like I did
> before, more or less? i.e. without having to determine the equation
> with the UnitStep function.
> Hope I've been clear enought. Many thanks.
> 
> Luca
> 
> 


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