Detect and Remove Singular Points

The pole of at is automatically identified and removed when plotting.

In[1]:=

Plot[1/x, {x, -3, 3}, ImageSize -> 400, PlotTheme -> "Frame"]

Out[1]=

Likewise for the poles of Tan[x].

In[2]:=

Plot[Tan[x], {x, 0, 4 Pi}, ImageSize -> 400, PlotTheme -> "Frame"]

Out[2]=

Show the asymptotes corresponding to the poles.

In[3]:=

{Plot[1/x, {x, -3, 3}, PlotTheme -> "Frame", ImageSize -> 250, ExclusionsStyle -> Directive[Gray, Dotted]], Plot[Tan[x], {x, 0, 4 Pi}, PlotTheme -> "Frame", ImageSize -> 250, ExclusionsStyle -> Directive[Gray, Dotted]]}

Out[3]=