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MathGroup Archive 2005

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Re: Summary: Which[] as Textbook Input, Plot[] Questions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54072] Re: Summary: Which[] as Textbook Input, Plot[] Questions
  • From: "Mariusz Jankowski" <mjankowski at usm.maine.edu>
  • Date: Wed, 9 Feb 2005 09:28:01 -0500 (EST)
  • Organization: University of Southern Maine
  • References: <cua5gn$hhl$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Matt, the answer to your first question is the function Piecewise introduced
in version 5 of Mathematica. As to the second, the Plot function evaluates
the given function at a discrete set of points to render it on the screen -
the selected set of points need not include discontinuities in the
function.

Regards, Mariusz



 

>>> Matt<anonmous69 at netscape.net> 2/8/2005 5:49:59 AM >>>
Hello,
   I apologize if the answer to this is somewhere glaringly obvious in
the documentation, however, after at least 4 hours pawing through both
the hardcover Mathematica 4.0 book by Wolfram and the in-program
Mathematica 4.1 documentation, I cannot find how I would annotate a
function that takes on different values based upon different domains.
To wit, something like:

Clear[f];
f[x_] := Which[x < 0, Sin[x]/x, x == 0, 1, x > 0, Sin[x]/x];
Plot[f[x], {x, -pi, pi}, AxesLabel -> {"x", "f[x]"};

The 'Which' function is great for actually evaluating something, but I
was looking for something along the lines of traditional mathematical
notation (such as one would write on a chalkboard or on a sheet of
paper), where a large left-bracket would be used and the various
definitions of the function for the various ranges would be
'constrained' by the bracket.

I'll try to illustrate what I mean, where the '|'s that I will use
should be interpreted as a single, large left-bracket:

       | Sin(x)/x, x < 0
f(x) = | 1, x = 0
       | Sin(x)/x, x > 0

Is there a way to do what I'm asking in Mathematica 4.1 (or even
above)?


As regards the Plot[] function, I'm puzzled as to why the following
doesn't give me an error when evaluated:

Clear[g];
g[x_] := 1/x;
Plot[g[x], {x, -5, 5}];

It seems as though it should, considering that x at zero is undefined.
However, Mathematica draws the graph as though the function were just
fine.

Thanks for any light you can shed on this,

Matt




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