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Re: How to plot discontinuous functions?


Aaron Fude wrote:

> 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?

Does it make really sense to define your function as vector valued?

If not, Plot does not face any major hurdles to spot the discontinuities 
of a real valued function.

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

Otherwise, you may have to tell Plot where to look for discontinuities 
and exclude them.

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

Regards,
-- Jean-Marc


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