Describe the domain of the function. $f(x)=\sqrt{-3x}$

A) $x\le -3$
B) $x\ge -3$
C) $x\ge 0$
D) $x\le 0$
E) all real numbers

The square root of a negative number is not a real number, therefore the expression under the root sign must be non-negative. We have $-3x\ge 0$ if and only if $x\le 0$ , since both 0 and any negative number squared are non-negative. Therefore, the domain of the function is $x\le 0$ , which is equivalent to choice D.