The function f is defined by f(x) = |x - 3| + 2. Which of the following statements is true about f at x = 3?

Core Concept

The absolute value function creates a corner at x = 3, where the left-hand derivative is -1 and the right-hand derivative is 1. Since these one-sided derivatives differ, f is not differentiable there, but f(3) = 2 exists and the limit as x approaches 3 equals 2, so f is continuous.