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Choose the function for which all of the following properties are true.

I. $\lim_{x \to0} \: f(x)=-\frac{1}{8}$

II. $\lim_{x \to2} \; f(x)=0$

III. $\lim_{x \to -4} f(x) \;$ is nonexistent

A

$f(x)=\cfrac{x-1}{x^2+8x+8}$

B

$f(x)=\cfrac{x-2}{x^2+8x+16}$

C

$f(x)=\cfrac{x^2-2}{4x+16}$

D

$f(x)=\cfrac{x-2}{x^2-16}$

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