AP Calculus ABmediummcq1 pt

Let $f(x)=\dfrac{x^2-9}{x-3}$ . Which statement about $x=3$ is true?

f

has a jump discontinuity at

x=3

f

has an infinite discontinuity at

x=3

f

is continuous at

x=3

f

has a removable discontinuity at

x=3

, and

\lim_{x\to 3} f(x)=6

Explanation

Core Concept

For $x\ne 3$ , $\frac{(x-3)(x+3)}{x-3}=x+3$ , so the limit is $6$ . The graph has a hole that could be filled by defining $f(3)=6$ , making the discontinuity removable.

Correct Answer

D $f$ has a removable discontinuity at $x=3$ , and $\lim_{x\to 3} f(x)=6$ .

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Practice Unit 1: Limits and Continuity Questions →

Let f(x)=x2−9x−3f(x)=\dfrac{x^2-9}{x-3}f(x)=x−3x2−9​. Which statement about x=3x=3x=3 is true?

Explanation

Core Concept

Correct Answer

More Unit 1: Limits and Continuity practice questions

Let $f(x)=\dfrac{x^2-9}{x-3}$ . Which statement about $x=3$ is true?