Question

is the union of two functions always a function?

Answer 1

If you could union the function, i.e. their domains and range aren't paradoxical, then the results would always be a function.

Answer 2

so...as long as the functions can be unioned...the result is a function...?

Answer 3

Yup, though to union two function, they both have to pass through some strict criteria. The domain of the second function must be smaller than the range of the first.