Answer
The red graph is the result.
Domain: $[2,\infty)$
Range: $[1,\infty)$
Work Step by Step
Starting with the graph of $y=\sqrt{x},$
1. horizontally shift to the right 2 units to obtain ... $y=\sqrt{x-2}$
2. vertically stretch by a factor of $2$ to obtain ... $y=2\sqrt{x-2}$
3. vertically shift upward 1 unit to obtain ... $y=2\sqrt{x-2}+1$
Plot several points of $y=\sqrt{x},$
perform the transformations 1-3 on each,
and join with a smooth curve ( red on the image).
Reading from the graph,
Domain: $[2,\infty)$
Range: $[1,\infty)$
