Let g(x) = |x² − 4|. Which of the following statements about g is true?

Core Concept

Correct. The expression inside the absolute value equals zero at x = −2 and x = 2, creating corners. The function is continuous everywhere because the left-hand and right-hand limits agree at every point, but at the corners the left and right derivatives differ (from the left the derivative approaches ∓4 and from the right it approaches ±4), so g is not differentiable there.