Answer
$f(x) $, domain $(-\infty, \infty)$, range $[0,\infty)$
$g(x) $, domain $(-\infty, \infty)$, range $(-\infty,4]$
Work Step by Step
Step 1. For function $f(x)=x^2$, shown as the red curve in the figure, we can identify its domain as $(-\infty, \infty)$ and its range as $[0,\infty)$
Step 2. For function $g(x)=-(x-1)^2+4$, shown as the blue curve in the figure, we can identify its domain as $(-\infty, \infty)$ and its range as $(-\infty,4]$
