## University Calculus: Early Transcendentals (3rd Edition)

$\mathrm{Domain:}\ \ (-\infty ,0]$ $\mathrm{See\:the\:graph\:below.}$
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.