The primary reason why the function f(x) = 1/x is discontinuous at x = 0 is which of the following?

Core Concept

The function f(x) = 1/x has a vertical asymptote at x = 0, which means that the graph approaches positive or negative ∞ as x approaches 0 from either side. This indicates a discontinuity at x = 0. The correct answer is B) The function has a vertical asymptote at x = 0. Options A, C, and D are incorrect because a hole would imply a removable discontinuity, and the function does not have a removable discontinuity at x = 0.