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AP Calculus AB 1.10 Exploring Types of Discontinuities Questions

Practise AP Calculus AB 1.10 questions by connecting piecewise formulas, graph features and limit behaviour to discontinuity types.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • distinguish holes, jumps and vertical asymptotes using limits and function values
  • locate and count discontinuities in piecewise and trigonometric functions

Covered syllabus points

LIM-2.A—Justify conclusions about continuity at a point using the definition

Question 1

[Maximum number: 1]

Let f be the function given by f(x)=x−22∣x−2∣f(x)=\frac{x-2}{2|x-2|}. Which of the following is true?

A

lim⁡x→2f(x)=12\lim _{x \rightarrow 2} f(x)=\frac{1}{2}

B

f has a removable discontinuity at x=2.

C

f has a jump discontinuity at x=2.

D

f has a discontinuity due to a vertical asymptote at x=2.

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