Answer
Graph "I" is the correct sketching.
Work Step by Step
For $y = \sqrt{x-3}-2,$
when $x = 3, y = -2$
The curve passes through $(3,-2)$
Since the graph of $y=\sqrt{x-3}-2$ is the same as the graph of $y=\sqrt{x}$ but with a horizontal translation of 3 units to the right and a vertical translation of 2 units down, graph "I" is the correct sketching.