Continuity and Limits Proofs

Question: Give an example of a function g such that g is continuous nowhere, but |g| is continuous everywhere?

Fairly simple set-up. I'm thinking that the best way to attack this would be with a piece-wise function (similar to the classic 1/q if rational, 0 if irrational), but I'm having trouble thinking of a function whose absolute value WOULD be continuous. I've done a couple of these problems with properties before, but I just am really stumped on this one. Any help is appreciated!

Thanks again,

Mike