FunctionContinuous

FunctionContinuous[f,x] tests whether f(x) is a real-valued continuous function for x∈Reals.

FunctionContinuous[f,x,dom] tests whether f(x) is a continuous function for x∈dom.

FunctionContinuous[{f1,f2,…},{x1,x2,…},dom] tests whether f1(x1,x2,…),f2(x1,x2,…),… are continuous functions for x1,x2,…∈dom.

FunctionContinuous[{funs,cons},xvars,dom] tests whether funs(xvars) are continuous functions for xvars∈dom restricted by the constraints cons. 

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