1. **State the problem:** We start with the parent function $f(x) = \sqrt[3]{x}$. We want to find the new function $g(x)$ after three transformations: - Reflection over the x-axis - Vertical compression by a factor of $\frac{1}{3}$ - Translation up by 5 units 2. **Recall the transformation rules:** - Reflection over the x-axis changes $f(x)$ to $-f(x)$. - Vertical compression by a factor $k$ changes $f(x)$ to $k f(x)$ where $0 < k < 1$. - Translation up by $c$ units changes $f(x)$ to $f(x) + c$. 3. **Apply the transformations step-by-step:** - Reflection over x-axis: $f(x) \to -\sqrt[3]{x}$ - Vertical compression by $\frac{1}{3}$: $-\sqrt[3]{x} \to -\frac{1}{3} \sqrt[3]{x}$ - Translation up 5 units: $-\frac{1}{3} \sqrt[3]{x} \to -\frac{1}{3} \sqrt[3]{x} + 5$ 4. **Write the final function:** $$ g(x) = -\frac{1}{3} \sqrt[3]{x} + 5 $$ 5. **Match with the options:** Option A and C are the same: $g(x) = -\frac{1}{3} \sqrt[3]{x} + 5$ **Answer:** Option A (or C) is correct.