Find the domain and rainge of this function (rational fn)

1. The problem statement, all variables and given/known data

Find domain and range of

f(x,y)=[itex]\frac{-3y}{x^{2}+y^{2}+1}[/itex]

2. Relevant equations



3. The attempt at a solution

It's quite obvious the the domain is R[itex]^{2}[/itex], because there are no possible values of x or y that would make the denominator 0.

But as for the range, my prof said that the range is from -3/2 to 3/2.

I can't figure out why. In my opinion, the range should be R[itex]^{3}[/itex], shouldn't it? I mean, there is no value y that would make the function not make sense. Also, x isn't even in the numerator and since we already accounted for it in the denominator, there is also no value x that would make the function not make sense. So how isn't the range R[itex]^{3}[/itex]?

Thanks in advance for the help.