The graph of \( y=-\sqrt[3]{x} \) is shifted 7 units up and 4 units right. Which equation represents the new graph? \( \begin{array}{l}y=-\sqrt[3]{x+4}+7 \\ y=-\sqrt[3]{x-7}+4 \\ y=-\sqrt[3]{x-4}+7 \\ y=-\sqrt[3]{x+7}+4\end{array} \)

To find the equation of the graph after shifting \( y = -\sqrt[3]{x} \) 7 units up and 4 units to the right, we need to apply the transformations step by step. 1. **Shift 4 units to the right**: To shift a graph to the right by \( h \) units, we replace \( x \) with \( x - h \). In this case, \( h = 4 \), so we replace \( x \) with \( x - 4 \): \[ y = -\sqrt[3]{x - 4} \] 2. **Shift 7 units up**: To shift a graph up by \( k \) units, we add \( k \) to the entire function. Here, \( k = 7 \), so we add 7 to the equation: \[ y = -\sqrt[3]{x - 4} + 7 \] Combining these transformations, the new equation representing the graph after the shifts is: \[ y = -\sqrt[3]{x - 4} + 7 \] Thus, the correct answer is: \[ \boxed{y = -\sqrt[3]{x - 4} + 7} \]