A function f(x) is said to be continuous at a point x = c if the following conditions are met: (1) the function is defined at x = c, (2) the limit of the function as x approaches c exists, and (3) the limit equals the value of the function at x = c. Which of the following statements is true about the function f(x)?

Core Concept

The primary reason this is true is that the function f(x) meets the three conditions for continuity at x = 0: it is defined at x = 0, the limit exists, and the limit equals the value of the function at x = 0. Options B and D are incorrect because the function is not defined at x = 1 and x = 2, respectively; option C is incorrect because the limit does not equal the value of the function at x = -1.