1. **Problem statement:** Given a transformed square root function with domain $x \geq -2$ and range $y \geq -5$, write a possible equation for this function. 2. **Recall the parent square root function:** The parent function is $y = \sqrt{x}$ with domain $x \geq 0$ and range $y \geq 0$. 3. **Transformation rules:** - Horizontal shifts: $y = \sqrt{x - h}$ shifts the graph $h$ units to the right if $h > 0$, or $|h|$ units to the left if $h < 0$. - Vertical shifts: $y = \sqrt{x} + k$ shifts the graph $k$ units up if $k > 0$, or $|k|$ units down if $k < 0$. 4. **Apply domain transformation:** The domain $x \geq -2$ means the inside of the square root must be $\geq 0$ when $x + 2 \geq 0$, so the function is shifted left by 2 units. 5. **Apply range transformation:** The range $y \geq -5$ means the graph is shifted down by 5 units. 6. **Write the transformed function:** $$ y = \sqrt{x + 2} - 5 $$ 7. **Explanation:** - The $x + 2$ inside the square root shifts the graph left by 2 units, changing the domain to $x \geq -2$. - The $-5$ outside shifts the graph down by 5 units, changing the range to $y \geq -5$. **Final answer:** $$ y = \sqrt{x + 2} - 5 $$