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

[skyturnred]

Homework Statement

Find domain and range of

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

Homework Equations

The Attempt at a Solution

It's quite obvious the the domain is R^{2}, 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^{3}, 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^{3}?

Thanks in advance for the help.

 

[WittyName]

The range isn't R^3 because the function f: R^2->R^1.