Answer
Domain:
$(-\infty, -\sqrt{3}] \cup [\sqrt{3}, +\infty)$
Range:
$(-\infty, 0]$
Work Step by Step
(a)
Use a graphing calculator to graph the given function. (Refer to the attached image below for the graph)
(b)
The domain is the set that contains all the x-values of the given function.
(Refer to the graph below.)
Note that the graph of the given function covers the x-values from the left up to $-\sqrt3$ and from $\sqrt3$ to the right.
Thus, the domain of the function is $(-\infty, -\sqrt{3}] \cup [\sqrt{3}, +\infty)$.
The range is the set that contains all the y-values of the given function.
Note that the graph of the given function covers the y-values from $0$ and below.
Thus, the range is $(-\infty, 0]$.
