Answer
Domain: x and y are real numbers which satisfy: $x^{2}-y \geq 0$
Range: $g(x,y) \geq 0$
Level curves: $y=x^{2}+c^{2}$ which are a series of parabolas
Work Step by Step
Function: $g(x,y) = \sqrt {x^{2}-y}$
Domain: x and y are real numbers which satisfy: $x^{2}-y \geq 0$
Range: $g(x,y) \geq 0$
Level curves: $g(x,y)=c$ (constant)
$\sqrt {x^{2}-y}=c$
$y=x^{2}+c^{2}$ which are a series of parabolas
For example, when $c=1$,
$y=x^{2}+1$ is shown in the figure.
