Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question
AP Calculus ABeasymcq1 pt

A function f(x) is defined for all real numbers except at x = 2, where it has a vertical asymptote. Which of the following best describes the continuity of f(x) at x = 2?

A.The function is continuous at x = 2.
B.The function is discontinuous at x = 2.
C.The function is continuous from the left at x = 2, but discontinuous from the right.
D.The function is discontinuous from the left at x = 2, but continuous from the right.

Explanation

Core Concept

The function has a vertical asymptote at x = 2, which means that the graph approaches positive or negative ∞ as x approaches 2 from either side. This indicates a discontinuity at x = 2. The correct answer is B) The function is discontinuous at x = 2. Options A, C, and D are incorrect because the function does not have a limit at x = 2 and is therefore not continuous.

Correct Answer

BThe function is discontinuous at x = 2.

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