A function f(x) is said to satisfy the Intermediate Value Theorem if for any two points x = a and x = b in the domain of the function, and for any value y between f(a) and f(b), there exists a point x between a and b such that f(x) = y. Which of the following statements is true about the function f(x)?

Core Concept

The primary reason this is true is that the Intermediate Value Theorem is a statement about the continuity of the function. The theorem states that if the function is continuous on the interval [a, b], then it satisfies the theorem. Option B is incorrect because differentiability is not a necessary condition for the theorem; option C is incorrect because the interval must be closed; option D is incorrect because the interval must be the interval [a, b] in question, not a different interval.