Is this a function? Is the set $\theta=\{\big((x,y),(3y,2x,x+y)\big):x,y ∈ \mathbb{R}\}$ a function? If so, what is its domain, codomain, and range?
This is probably a dumb question. I understand what a function is, but the three elements in the ordered pair got me confused.

Yes it is, presumably one from $\mathbb{R}^2$ to $\mathbb{R}^3$, although the domain and codomain could potentially be smaller. You have an ordered pair in which the first element is itself an ordered pair (of real numbers), and the second is an ordered triple (of real numbers).
I'm used to codomain and range meaning the same thing. If you meant image for one of them, I can't think of a better description than $\{(3y,2x,x+y):x,y\in\mathbb{R}\}$.
