Find the Domain and Range g(x,y)=x square root of y

$g (x, y) = x \sqrt{y}$

Set the radicand in $\sqrt{y}$ greater than or equal to $0$ to find where the expression is defined.

$y \geq 0$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Determine the domain and range.

Domain: $[0, \infty), {y | y \geq 0}$

Range: $[0, \infty), {y | y \geq 0}$