...which of the following pairs of statements about the continuity of the piecewise function is true?

A

$f(x)$ is continuous at all points in the domain. The limit exists for each point of $f(x)$ in the domain.

B

$f(x)$ is continuous at all points on $(-1,0)$. Since there is a removable discontinuity at $x=0$, the limit does not exist for each point of $f(x)$ in the domain.

C

$f(x)$ is continuous at all points on $(-1,1)$. The limit exists for each point of $f(x)$ in the domain.

D

$f(x)$ is continuous at all points on $(0,1)$. The limit exists for each point of $f(x)$ in the domain.