Yeah, you can pick a point within the domain, to show continuity in that interval, and I would take a point in the undefined interval to show that the function is undefined there. These aren't "proofs" per se as much as they are verification. I'm not sure if you've touched epsilon-delta proofs? There are better ways of proving where a function is continuous, but it depends on what level of math you are at. Follow your course's example on that note.

When you are looking for domains or continuity, always look for places that would mess up the graph of the function, like zero-denominators, possible negative radicands, etc. These things can hack your domain in half, like the root here restricted the domain.

For example

, would have the domain

with open brackets because 0 is

*not defined*.