Continuity of a Function

Question

Let f(x,y) = ( 3*(x^2)*y ) / ( (x^2) + (y^2) )

Where is f continuous?

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We've been taught that a polynomial in x, y is continuous everywhere on R^2

How do we find the continuity of a function like this when there are 2 different functions kind-of-terms in both numerator and the denominator?

Answer 1

Any function regardless of the number of variable is discontinuous when the denominator is equal to zero.