ANSWER
![y = \sqrt[3]{x + 4} - 1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/t3mtwp4pqt02eip9aomh5w5wqvkopzby6k.png)
Step-by-step explanation
The given function is
![y = \sqrt[3]{x}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/o5zyqninhsxuofzk0phaqmtw14ov8g4b31.png)
The transformation
![y = \sqrt[3]{x + k} - c](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jevdqbqne2nnyujlz1cqfqm23903gzva6e.png)
shifts the graph of the base function k units left and c units down.
Since the graph is shifted 4 units left, k= 4
Also, the graph is shifted 1 unit down.
This implies that c=1
The new equation is
![y = \sqrt[3]{x + 4} - 1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/t3mtwp4pqt02eip9aomh5w5wqvkopzby6k.png)
The last option is correct.