Answer
See graph (red).
domain $[1, \infty)$, range $(-\infty, 0]$.
Work Step by Step
Step 1. To obtain the graph of $f(x)=-4\sqrt {x-1}$ from $y=\sqrt x$, shift the curve 1 unit to the right, stretch vertically by a factor of 4, then reflect across the x-axis. See graph (red).
Step 2. We can find the domain $[1, \infty)$ and the range $(-\infty, 0]$.
