       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)
• 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).
> 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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