APFIVE Types of Discontinuities in Rational Functions
The function $$\displaystyle h(x) = \frac{x^2 - 9}{x^2 - 2x - 3}$$ has a discontinuity at $$\displaystyle x = 3$$. Which of the following best describes the behavior of $$\displaystyle h$$ at this discontinuity?
A
There is a vertical asymptote at $$\displaystyle x = 3$$
B
$$\displaystyle \lim_{x \to 3} h(x) = \infty$$
C
There is a removable discontinuity (hole) at $$\displaystyle x = 3$$
D
The function is continuous at $$\displaystyle x = 3$$
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