Answer
Continuous: A,D,E,F
Work Step by Step
A - It is continuous on its domain (the function is not defined at $x=2$, so it is not in the domain).
B - It is not continuous at $x=2$ because the left limit is not the same as the right limit (the limit is not defined at $x=2$, and the function is).
C - As in B, $f(2)$ is defined, but the limit at $2$ does not exist.
D - It is continuous because the domain is $(-\infty,1]\cup[2,\infty)$, and it is left-continuous at 1, right-continuous at 2.
E - Continuous. At $x=2$, a limit exists and equals $f(2)$.
F - Continuous. The domain is an open interval $(a,\infty)$,
