is an option that specifies where to exclude in regions used by functions like Plot, Plot3D, and NIntegrate.


  • The following settings specify what to exclude:
  • Noneno exclusions
    Allall computed exclusions
    Automaticautomatically computed exclusions
    "Discontinuities"computed jump discontinuities
    "Singularities"computed singularities
    lhs==rhsexplicitly defined by an equation
    {lhsrhs,cond}explicitly defined by an equation and a condition
    {spec1,spec2,}union of exclusions given by speci
  • Exclusions->Automatic is effectively equivalent to Exclusions->All if $PerformanceGoal is "Quality", and to Exclusions->None otherwise.
  • For a domain defined by n variables, exclusions must be of dimension .
  • For a domain defined by one variable, Exclusions->{x1,x2,} will exclude the points xi.
  • Exclusions"Discontinuities" typically includes piecewise discontinuities and branch-cut discontinuities.
  • Exclusions"Singularities" typically includes poles and essential singularities.
  • The automatically computed exclusions will typically include potential discontinuities and singularities, including removable discontinuities and singularities.
  • For plotting functions, ExclusionsStyle specifies how to draw exclusions and their boundaries.


open allclose all

Basic Examples  (5)

Exclude portions of a surface where it has jumps:

Leave the surface entirely connected:

Exclude portions of a curve where it has jumps:

Exclude a fixed set of points:

Specify where the function is discontinuous:

Scope  (6)

Exclude areas where the function has jump discontinuities:

Exclude areas where the function has singularities:

Specify the style to use for excluded portions of a curve:

Use dotted lines to connect portions of the curve and red points where there are jumps:

Use transparency to show excluded portions of the surface:

Use thick, red lines around the edges of the excluded portions of the surface:

Possible Issues  (2)

Removable singularities may be detected:

Use Exclusions->None to ignore the singularity:

Sinc[x] is equivalent to Sin[x]/x but does not have a singularity at :

Some discontinuities and singularities may not be detected:

Specify where the discontinuities are:

Introduced in 2007
Updated in 2016