1) f is not continuous at x = a because f(a) is undefined. That is, the function f is NOT DEFINED at x = a. (There's no output!)

2) f is not continuous at x = a because the limit as x --> a of f(x) does not exist. In order for the limit as x --> a of f(x) to exist, both left and right-ended limits must exist and be equal in value. For this function, the limit as x -->a of f(x) from the left is NOT EQUAL to the limit as x -->a from the right of f(x).

3) f is not continuous at x = a because the limit as x --> a of f(x) does not equal f(a). (Note how the first two criteria for continuity hold true here but the third one doesn't!)