The function value at x=0 is different, so this function must be discontinuous. Of the four options, only B says discontinuous, but can it be derived? It is not derivable at x=0, but it should be derivable at x≠0? Continuous functions are definitely derivable, but conversely, are discontinuous functions necessarily non-derivable? I don't think so, the derivative is the tangent of the curve, and the curve that is not at the discontinuity should still have a tangent, right? So I think we should choose D.