Answer
please see image
(graph of g(x) is red)
.
Work Step by Step
$f(x)=\sqrt{x}$
Using desmos.com, we graph f(x) (blue dashed graph)
By hand,
we select some values for x and make a table with
x ... f(x) as columns.
(In the screenshot, the table is to the left )
Plotting the points (x,f(x)) and joining them with a smooth curve, we have the graph of f(x).
Using Table 2.4, Summary of Transformations, we see that
$g(x)=\sqrt{x}+2=f(x)+2$
belongs to the group:
"Vertical shifts
$y=f(x)+c$
Raise the graph of $f$ by $c$ units.
$c$ is added to $f(x)$."
So,
we add another column to our table, which will contain $f(x)+2.$
We plot the points ( x, f(x)+2 ),
join them with a smooth curve,
(red solid line on the screenshot),
and we have the graph of g(x)