For part (i), the modulus function $|x|$ is defined for all real numbers, so its domain is $\mathbb{R}$. Since $|x| \geq 0$ for all $x$, multiplying by -1 gives $-|x| \leq 0$, making the range all non-positive real numbers.

For part (ii), the square root function requires $9-x^2 \geq 0$, which gives $x^2 \leq 9$ or $-3 \leq x \leq 3$. The maximum value occurs at $x=0$ giving $\sqrt{9}=3$, and minimum at $x=\pm 3$ giving $\sqrt{0}=0$.