Final answer:
The graph of y = ∛(8x - 64) - 5 compared to the parent cube root function is transformed by being stretched by a factor of 8, translated 8 units to the right, and 5 units down.
Step-by-step explanation:
The graph of y = ∛(8x - 64) - 5 is transformed compared to the parent cube root function, y = ∛x. First, we look at the factor in front of 'x'. In the expression 8x - 64, '8' indicates a stretch factor, so the graph is stretched by a factor of 8. Next, you need to identify the translations. The term '-64' inside the cube root suggests a horizontal shift, and since we are subtracting from 'x', this will be a rightward shift.
To determine the exact translation, we set the inside of the cube root to zero: 8x - 64 = 0; solving for 'x' gives us 'x = 8', which means the graph is translated 8 units to the right.
Lastly, the '-5' outside of the cube root affects the vertical translation, moving the graph downwards by 5 units.