Final answer:
The equation of y=x³ with the given transformations is y=8(x-2)³-7.
Step-by-step explanation:
The equation of y=x³ after the given transformations is y=8(x-2)³-7.
To understand how these transformations affect the original function y=x³, we can break it down step by step. First, the vertical stretch by a factor of 8 multiplies the y-values by 8. So, the equation becomes y=8x³.
Then, the horizontal shift 2 units to the right is represented by (x-2), which shifts the graph of the function to the right by 2 units. Finally, the vertical shift 7 units down is represented by -7, which shifts the graph downward by 7 units.
Combining all the transformations, the equation becomes y=8(x-2)³-7.