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RE: Define a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34570] RE: [mg34556] Define a function
  • From: "DrBob" <majort at cox-internet.com>
  • Date: Wed, 29 May 2002 02:44:10 -0400 (EDT)
  • Reply-to: <drbob at bigfoot.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Here's a simple solution:

f[x_] := Which[
    x < 10, 0,
    x < 20, x,
    True, x/2
    ]
Plot[f[x], {x, 0, 30}]

And here's another:

ClearAll[f]
f[x_] /; x < 10 := 0
f[x_] /; x < 20 := x
f[x_] := x/2
Plot[f[x], {x, 0, 30}]

>>I have to define different functions for different ranges of the
variable x.

It's a subtle point perhaps, but in both cases f is ONE function,
defined for all x.  (REALLY all x, the way I've done it...)  For
instance, evaluate

f["2"]
f[""]
f[{1,2}]

What you mean is that the functional form, expression, or computation
rule is different, for different ranges of the variable.

Bobby Treat

-----Original Message-----
From: Michael Popp [mailto:popp.michael at gmx.at] 
To: mathgroup at smc.vnet.net
Subject: [mg34570] [mg34556] Define a function

Hello

I want to define a function in Mathematica. But just f[x_]:=...  does
not
work, because I have to define different functions for different ranges
of
the variable x.
For example:

x < 10:           f(x) = 0
10 < x < 20:  f(x) = x
20 < x:          f(x) = x/2

How to do this?

Thanks, greetings
Michael








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