Plot[Tan@x, {x, -2 \[Pi], 2 \[Pi]}, ExclusionsStyle -> {Dashed, Red}, Exclusions -> "Discontinuities"]
How to draw the asymptotes of the tangent function as red dashed lines?
Maybe something like this:
Plot[Tan@x, {x, -2 Pi, 2 Pi}, ExclusionsStyle -> Directive[Dashed, AbsoluteThickness[5], Red]]
FWIW, the documentation for ExclusionsStyle spells this out.
ExclusionsStyle