The Intermediate Value Theorem states that if a function f(x) is continuous on the closed interval [a, b] and k is any value between f(a) and f(b), then there exists a value c in [a, b] such that f(c) = k.

Core Concept

The Intermediate Value Theorem states that if a function f(x) is continuous on the closed interval [a, b] and k is any value between f(a) and f(b), then there exists a value c in [a, b] such that f(c) = k. The theorem does not apply to functions that are not continuous on the closed interval [a, b]. Option A is incorrect because the theorem applies to functions that are continuous on a closed interval. Option B is incorrect because the theorem does not state that the function is continuous on the entire real line. Option C is incorrect because the theorem does apply to functions that have a discontinuity in the closed interval [a, b].