The function f(x) = 1/x has a discontinuity at x = 0 due to

Core Concept

The function f(x) = 1/x has a vertical asymptote at x = 0 since the function approaches infinity as x approaches 0 from the right and approaches negative infinity as x approaches 0 from the left. This is the primary reason why the function is discontinuous at x = 0. Options A and B are incorrect since the function does not have a hole or a jump at x = 0. Option D is incorrect since the function approaches infinity and negative infinity as x approaches 0, not a horizontal asymptote.