This appears to be three different functions:
, for x < 0
, for x < 2
, for x > 2
Is that what you have? Not sure what your equation is. Can you clarify that?
For the continuity rules #2 & #3:
#2 says that as the x values on the graph of f(x) get closer and closer to c, there is a guaranteed y value associated with each of those x values
#3 says that if you evaluate f(x) at c, meaning you plug the the value of c into the x values of your function, then the answer you get will be the limit of your function.
Hope that helps!