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AP Calculus AB/Unit 1: Limits and Continuity
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Types of Discontinuities in Rational Functions

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For the function h(x)=x2−9x2−2x−3h(x) = \frac{x^2 - 9}{x^2 - 2x - 3}, which of the following statements best describes the discontinuity at x=3x = 3?

A

There is a vertical asymptote at x=3\displaystyle x = 3

B

There is a removable discontinuity (hole) at x=3\displaystyle x = 3

C

lim⁡x→3h(x)=∞\displaystyle \lim_{x \to 3} h(x) = \infty

D

The function is continuous at x=3\displaystyle x = 3

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