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

AP Calculus ABmediummcq1 pt

Let $f(x)=\dfrac{x^2-x-2}{x-2}$ for $x\ne 2$ . What value of $f(2)$ makes $f$ continuous at $x=2$ ?

A.

2

B.

0

C.

3

D.No such value exists

Explanation

Core Concept

Factor: $x^2-x-2=(x-2)(x+1)$ , so $f(x)=x+1$ for $x\ne 2$ and $\lim_{x\to 2} f(x)=3$ . Defining $f(2)=3$ removes the discontinuity.

Correct Answer

C $3$

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