The graph of f(x) = |x| is discontinuous at x = 0 because

Core Concept

The graph of f(x) = |x| has a jump discontinuity at x = 0 since the left and right limits are different. This is the primary reason why the function is discontinuous at x = 0. Option A is incorrect since the function approaches different limits as x approaches 0 from the left and right. Option C is incorrect since the discontinuity is not removable. Option D is related but incorrect since the function is defined at x = 0.