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Mathematica Plot function can detect exclusion points automatically. How was that realized? How can I generalize that to included discontinuity of DiracDelta functions as well?

For example, I would like to have something like

ExclusionPoints[UnitStep[x + 2] + DiracDelta[x - 1] + Piecewise[{{1, x > 0}}], x]
(* returns {-2, 0, 1} *)
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