       Re: How to plot discontinuous functions?

• To: mathgroup at smc.vnet.net
• Subject: [mg90149] Re: How to plot discontinuous functions?
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Tue, 1 Jul 2008 06:56:22 -0400 (EDT)
• References: <g4a6tv\$8uh\$1@smc.vnet.net>

```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}]

Generally, it is not possible to detect discontinuities numerically.
(Is the function 1/(1 + Exp[10000 x]) continuous at 0?)  Still,
Mathematica does a pretty good job of finding them by analysing the
expression the function is made of.  When it fails to detect a
discontinuity, you can specify it manually:

Plot[f[x], {x, 0, 2}, PlotRange -> {0, 3}, Exclusions -> {1}]

(Look up Exclusions)

>
> Defined via Piecewise, it does, but in my experience, not always:
> f[x_] := Piecewise[{{{1, 1}, x < 1}}, {2, 2}];
> Plot[f[x][], {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
>

```

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