To find the new equation of the graph of the function y = x³ after it has been shifted, we need to take into account the transformations described.
1. **Horizontal Shift**: Shifting the graph horizontally to the left by 4 units means adding 4 to the x-coordinates. This transforms the original function as follows: y = (x + 4)³.
2. **Vertical Shift**: Shifting the graph vertically downward by 5 units means subtracting 5 from the y-coordinates. So, we adjust the equation from the previous step: y = (x + 4)³ - 5.
Therefore, the final equation that defines the graph of y = x³ after these transformations is:
y = (x + 4)³ – 5