Answer
please see image
(graph of h(x) is red)
.
Work Step by Step
$f(x)=\sqrt{x}$
Using desmos.com, we graph f(x) (blue dashed graph)
By hand, we would 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
$h(x)=-\sqrt{x+2}=-f(x+2)$
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 then
"Reflection about the x-axis $y=-f(x)$
Reflect the graph of $f$ about the x-axis. $f(x)$ is multiplied by $-1$ "
So,
using our table (x, f(x))
We plot the points ( $x-2,\ -f(x)$ ),
moving the originals to the left and flipping them across the x-axis.
Join them with a smooth curve,
(red solid line on the screenshot),
and we have the graph of h(x).
