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]=
