ANSWER
![g(x) = - √(x + 3) + 8](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5gl0al6m1qmib7k4r7g4o8eclei50rty38.png)
Step-by-step explanation
The given function is
![f(x) = - 2 √(x - 3) + 8](https://img.qammunity.org/2020/formulas/mathematics/middle-school/l26zj8b0zxkwa87yxsw1zoknzelmhmkbp0.png)
The vertex of this function is (3,8)
This function opens downwards so its range is
![y \leqslant 8](https://img.qammunity.org/2020/formulas/mathematics/middle-school/c7zu1a3793m8uh7ryt8qlvwk19ygwcsa8f.png)
The function
![g(x) = - √(x + 3) + 8](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5gl0al6m1qmib7k4r7g4o8eclei50rty38.png)
also has vertex (-3,8)
This function is also reflected in the x-axis. Its range is;
![y \leqslant 8](https://img.qammunity.org/2020/formulas/mathematics/middle-school/c7zu1a3793m8uh7ryt8qlvwk19ygwcsa8f.png)
The correct answer is C