We have the following:
[tex]y=-4+3\sqrt[]{x+3}[/tex]The domain is the input values or the values that x can take and the range is the output values or values that y can take,
For the domain, the value of x cannot be such that it makes what is inside the root less than 0, therefore
[tex]\begin{gathered} x+3\ge0 \\ x\ge-3 \\ D=\lbrack-3,\infty) \end{gathered}[/tex]For the range:
Since the second term, the one that contains the root, its minimum value is 0, then the range would be
[tex]\begin{gathered} y\ge-4 \\ R=\lbrack-4,\infty) \end{gathered}[/tex]Therefore, the answer is A)