Answer
$\mathrm{Domain:}\ \ (-\infty ,0]$
$\mathrm{See\:the\:graph\:below.}$
Work Step by Step
We can take the square root only of positive numbers. Find the non-negative values of the radical by using:
$\sqrt{f(x)}\quad \Rightarrow \quad \:f(x)\ge 0$
$-x\ge \:0$
Multiply both sides by -1 and reverse the inequality.
$x\le \:0$
So, the function domain is, $\ (-\infty ,0].$
The graph of the given function $\ y=\sqrt{-x}\ $ is similar to the graph of the function $\ y=\sqrt{x}\ $, except that it is reflected over the $\mathrm{y-axis}.$
See the graph below.
