Mathematica Exclude Singularities in Plot

#Mathematica

Mathematica Plot might include some non-existant lines sometimes, Exclusions is the potion for it.

Mathematica Plot function brings in weird lines sometimes.

Here is an example of it. I plot

$$ f(x) = \frac{1}{1-0.3 x}. $$

Plot[1/(1 - 0.3 x), {x, 2, 5}, Frame -> True,
 FrameLabel -> {"x", "1/(1-0.3 x)"}, ImageSize -> Large,
 PlotLabel -> "Function: 1/(1-0.3 x)"]

What we get is a plot

A plot with singularity point. Mathematica Plot brings in an extra line at the singularity.

A plot with singularity point. Mathematica Plot brings in an extra line at the singularity.

This vertical line at $x=3$ is not real. To eliminate this line, we can exclude the singularity point when plotting, using Exclusions.

Plot[1/(x - 3), {x, 2, 4}, Frame -> True,
 FrameLabel -> {"x", "1/(x-3)"}, ImageSize -> Large,
 PlotLabel -> "Function: 1/(x-3)", Exclusions -> {3}]

The plot we get now is much better.

With Exclusions->{3}

With Exclusions->{3}

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