Need help with range of a two variable function

[esmeco]

Homework Statement

Given z=f(x,y),where f(x,y) is - say- f(x,y)=x^2-2y+4 how would I go about finding the range of the function like it was done for f(x)=y,when f(x)=x^2-1 ,for example,we would put x^2-1=y and solve for x?

 

[HallsofIvy]

No, the range of f(x,y) is the set of possible values of f no matter what x and y are. Suppose y= 0. What are the possible values of f(x,0)= x²- 1? Suppose x= 0. What are the possible values of f(0,y)= -y- 1?