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Which of the following sets of statements accurately describes​ continuity of the above graph of $f(x)$?

A

$f(x)$ is continuous for all $x$: $(-\infty,-1)$U$(-1,0)$U$[0,2]$U$(2, \infty)$.

B

$f(x)$ is continuous for all $x$: $(-\infty,-1)$U$(-1,0)$U$[0,2)$U$(2, \infty)$.

C

$f(x)$ is continuous for all $x$: $(-\infty,-1)$U$[-1,0)$U$[0,2)$U$(2, \infty)$.

D

$f(x)$ is continuous for all $x$: $(-\infty,-1)$U$[-1,0]$U$[0,2)$U$(2, \infty)$.

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