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AP Calculus AB 1.11 Defining Continuity at a Point Question Bank

Practise AP Calculus AB 1.11 continuity questions by connecting one-sided limits, two-sided limits and function values.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • verify continuity by checking matching one-sided limits, the two-sided limit and f(a)
  • apply continuity to compositions and limits of transformed functions

Covered syllabus points

LIM-2.A—Justify conclusions about continuity at a point using the definition—Topic 1.11

1.11 Defining Continuity at a Point question 1

[Maximum number: 1]

If lim⁡x→af(x)=f(a)\lim _{x \rightarrow a} f(x)=f(a), then which of the following statements about f must be true?

A

f is continuous at x=a.

B

f is differentiable at x=a.

C

For all values of x, f(x)=f(a).

D

The line y=f(a) is tangent to the graph of f at x=a.

E

The line x=a is a vertical asymptote of the graph of f.

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