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AP Calculus AB 1.10 Exploring Types of Discontinuities Question Bank

Practise AP Calculus AB 1.10 discontinuity questions by classifying holes, jumps and vertical-asymptote behaviour from formulas or graphs.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • classify removable, jump and infinite discontinuities from formulas, tables and graphs
  • count discontinuity locations by checking domain breaks and one-sided behaviour

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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