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.
Each pair gives a point on the graph of f(x).
(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
$g(x)=\displaystyle \frac{1}{2}\sqrt{x+2}=\frac{1}{2}f(x+2)$
is obtained by
"Horizontal shifts $y=f(x+c)$
Shift the graph of $f$ to the left $c$ units. $x$ is replaced with $x+c$."
and
"Vertical stretching or shrinking $y=cf(x), 0 < c <
1$
Multiply each y-coordinate of $y=f(x)$ by $c$, vertically shrinking the graph of $f$.
$f(x)$ is multiplied by $c,\ 0 < c < 1$"
So,
using our table (x, f(x))
we plot the points ( $x-2,\ \displaystyle \frac{1}{2}f(x)$ ),
moving the originals to the left,
and then vertically shrinking the graph of $f ($with $\displaystyle \frac{1}{2}f(x)$)
Join them with a smooth curve,
(red solid line on the screenshot),
and we have the graph of g(x).
