Answer
The range is $y\geq -4$.
The graph is shown below.
Work Step by Step
The given function is
$g(x)=\sqrt{x}-4$
Use the domain of $g$, $x\geq 0$, to make a table of values.
Plot the ordered pairs.
Draw a smooth curve through the points, starting at $(0,-4)$.
From the graph, the range of $g$ is $y\geq -4$.
