I guess this has already be answered.
Plot[1/(x^3 - 2 x^2), {x, -2, 4}, Exclusions -> True] Plot[1/(x^3 - 2 x^2), {x, -2, 4}, Exclusions -> 2] I cannot understand why I have to specify the position of discontinuity (2nd plot) in order to get rid of the vertical line at x=2 (which exists in the first plot). Exclusions->True is not for detect the position of discontinuities? The function is rather simple.
Plot seems to only do exclusions automatically for certain functions, such as Piecewise and some functions with branch cuts. For algebraic functions it seems to require an equation be passed to the Exclusions options.
I suspect that Plot determines exclusions in the same way as mesh points, by tracking when a zero is crossed. It seems simple enough to make an equation that defines which points are to be excluded:
Plot[f, {x, a, b}, Exclusions -> {1/f == 0}] If you like, you can put this in a wrapper:
ClearAll[addExcl]; SetAttributes[addExcl, HoldAll]; addExcl[Plot[f_, {x_, a_, b_}, opts___?OptionQ]] := Plot[f, {x, a, b}, Exclusions -> Flatten@{Thread[1/f == 0]}, opts] Examples:
addExcl@Plot[Tan[x]/(x^3 - 2 x^2), {x, -2, 4}] 
addExcl@Plot[{Tan[x]/(x^3 - 2 x^2), 1/(1 - Log[x])}, {x, -2, 4}] 
1/(x-2). - dimitris, Here is the advice on how to do it from the docs (Plot> "Options" > "Exclusions"):Plot[1/(x^3 - x + 1), {x, -2, 2}, Exclusions -> {x^3 - x + 1 == 0}]$\endgroup$x == 0is not excluded per se -- the plot just goes beyond thePlotRangeand re-enters on the same side. It would be nice ifExclusions -> Allwould callNSolveor do something extra. It does not seem to. $\endgroup$Exclusions, the settingsAllandTrueare synonymous withAutomatic. In the trace,foo = Trace[Plot[1/(x^3 - 2 x^2), {x, -2, 4}, Exclusions -> True], TraceInternal -> True];, this happens:If[Graphics`PerformanceTuningDump`exclusions === All || Graphics`PerformanceTuningDump`exclusions === True, Graphics`PerformanceTuningDump`exclusions = Automatic]. $\endgroup$