Answer
Graph "F" 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 left and a vertical translation of 2 units up, graph "F" is the correct sketching.