Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question
AP Calculus ABmediummcq1 pt

The graph of f(x) = |x| is discontinuous at x = 0 because

A.D) The function is not defined at x = 0
B.A) The function approaches a finite limit as x approaches 0
C.B) The function has a jump discontinuity at x = 0
D.C) The function has a removable discontinuity at x = 0

Explanation

Core Concept

The graph of f(x) = |x| has a jump discontinuity at x = 0 since the left and right limits are different. This is the primary reason why the function is discontinuous at x = 0. Option A is incorrect since the function approaches different limits as x approaches 0 from the left and right. Option C is incorrect since the discontinuity is not removable. Option D is related but incorrect since the function is defined at x = 0.

Correct Answer

CB) The function has a jump discontinuity at x = 0

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