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Re: How to plot discontinuous functions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90158] Re: [mg90135] How to plot discontinuous functions?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Tue, 1 Jul 2008 06:58:05 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200806300853.EAA09174@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Here are two ways for your example -- first, build the function using 
Boole (much as one does when working with Laplace transforms); second, 
use the Exclusions option:

   Plot[1+Boole[x>1],{x,0,3},PlotRange->{{0,2},{0,3}}]

   f[x_]:=Piecewise[{{{1,1},x<1}},{2,2}];
   Plot[f[x][[1]],{x,0,2},PlotRange->{0,3},Exclusions->1]

   f[x_]:=If[x<1,1,2];
   Plot[f[x],{x,0,2},PlotRange->{0,3},Exclusions->1]

Aaron Fude wrote:
> Hi,
> 
> If a function is defined via If, then when plotted it does not
> acknowledge the discontinuity. E.g.
> 
> f[x_] := If[x < 1, 1, 2];
> Plot[f[x], {x, 0, 2}, PlotRange -> {0, 3}]
> 
> Defined via Piecewise, it does, but in my experience, not always:
> f[x_] := Piecewise[{{{1, 1}, x < 1}}, {2, 2}];
> Plot[f[x][[1]], {x, 0, 2}, PlotRange -> {0, 3}]
> 
> How do I make the Plot function try to acknowledge the discontuity by
> not connecting the left limit and the right limit?
> 
> Thanks,
> 
> Aaron
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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