       Re: Piecewise functions

• To: mathgroup at smc.vnet.net
• Subject: [mg51561] Re: [mg51553] Piecewise functions
• From: DrBob <drbob at bigfoot.com>
• Date: Sat, 23 Oct 2004 00:21:41 -0400 (EDT)
• References: <200410220222.WAA07319@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Clear@y
y[x_] /; x > 3 := x
y[x_] /; -1 < x < 3 := -x
y[_] := 1
Plot[y@x, {x, -2, 4}]

y/@{-1,3}

{1,1}

or

Clear@y
y[x_] := Which[x > 3, x,
-1 < x < 3, -x,
True, 1]
Plot[y@x, {x, -2, 4}]

y/@{-1,3}

{1,1}

or

Clear@y
y[x_] := 1 + (-1 - x) UnitStep[x + 1] + 2x UnitStep[x - 3]
Plot[y@x, {x, -2, 4}]

y/@{-1,3}

{1,3}

The last form has big advantages if you want to differentiate or integrate the function.

Bobby

On Thu, 21 Oct 2004 22:22:10 -0400 (EDT), Luca <luca at nospam.it> wrote:

> 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
>
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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