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If $\mathop {\lim }\limits_{x \to a^-}{ f\left( x \right)} =\infty$ and $\mathop {\lim }\limits_{x \to a^+} { f\left( x \right)}=-\infty$, then

A

$y=a$ is a horizontal asymptote of $f\left( x \right)$.

B

$x=a$ is a vertical asymptote of $f\left( x \right)$.

C

$f(x)$ is continuous at $x=a$ .

D

$f(a)$ is undefined.

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