SOLUTION: What is the domain and range of F(x,y)= √(16-x^2-16y^2 )

That is the equation of a hemisphere in the four upper octants.  
Its domain is the set of points in or on the circle in the xy-plane 
with center at the origin and radius  or 4, that is, 
the domain is this circular disk: 

{ }

The range is the set of z-values

{ } 

which can also be written in interval notation as 



Edwin