ANSWER
domain:
[tex]x \geqslant - 3[/tex]
Range
[tex]y \leqslant - 2[/tex]
EXPLANATION
The given function is
[tex]f( x) = - \sqrt{x + 3} - 2[/tex]
This base of this function is
[tex]y = \sqrt{x} [/tex]
This function has been shifted to the left 3 units and down 2 units.
This function is reflected in the x-axis.
Therefore graph starts at (-3,-2) and move down forever.
The domain is obtained using the expression under the radical sign.
It must be greater than or equal to zero.
[tex]x + 3 \geqslant 0[/tex]
[tex]x \geqslant - 3[/tex]
The range is
[tex]y \leqslant - 2[/tex]
