A function f(x) is said to be continuous on the closed interval [a, b] if it is continuous at every point in the interval. Which of the following statements is true about the function f(x) on the interval [0, 2]?

Core Concept

The primary reason this is true is that the continuity of the function at a point is a necessary but not sufficient condition for its continuity on an interval. The function must also be continuous at the endpoints of the interval in order to be continuous on the entire interval. Option A is incorrect because the function may be discontinuous at the endpoints; option C is incorrect because the function may be discontinuous at other points in the interval; option D is incorrect because the function may be discontinuous at other points in the interval.