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AP Calculus BC 1.10 Exploring Types of Discontinuities Questions

Classify discontinuities and use one-sided limits, two-sided limits and function values to justify whether a function is continuous.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • connect derivative evidence to function behavior and interpretation
  • justify a calculus conclusion from symbolic, graphical or contextual evidence

Covered syllabus points

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

Question 1

[Maximum number: 1]

The graph of y=f(x) is shown above. Which of the following is true?

A

lim⁡h→0f(a+h)−f(a)h\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h} exists.

B

lim⁡x→a+f(x)≠lim⁡x→a−f(x)\lim _{x \rightarrow a^{+}} f(x) \neq \lim _{x \rightarrow a^{-}} f(x)

C

lim⁡x→af(x)≠f(a)\lim _{x \rightarrow a} f(x) \neq f(a)

D

lim⁡x→af(x)\lim _{x \rightarrow a} f(x) does not exist.

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