## Thomas' Calculus 13th Edition

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
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.