Sort: bounded or unbounded domain?

Bounded domain: $f(x,y) = \sqrt{4 - x^{2} - y^{2}}$, $f(x,y) = \ln(1 - x^{2} - y^{2})$, $f(x,y) = \sqrt{9 - x^{2} - 4y^{2}}$

Unbounded domain: $f(x,y) = x^{2} + y^{2}$, $f(x,y) = 1/(x+y)$, $f(x,y) = \sin(x)\cos(y)$

Square roots and logs restrict the domain to regions where the argument is non-negative/positive.