Final answer:
The given function seems to be a transformation of the cube root function. Assuming an error in its expression and correcting it to y = 8∛(x - 84) - 5, it would be stretched by a factor of 8 and translated 84 units right and 5 units down.
Step-by-step explanation:
The question asks us to compare the graph of the given function Y = 8x - 84 - 5 to the parent cube root function, which seems to be incorrectly expressed in the question, as it typically would be written as y = ∛x or y = x^(1/3). Assuming that the intended function was a transformation of the cube root function, we can identify the changes made to the cube root function. A stretch factor would be associated with the coefficient in front of the variable x. A translation (shift) would be associated with the constants added or subtracted to the variable x or to the function as a whole, respectively. If these were the intended transformations, then the function y = 8x^(1/3) - 84 - 5 would indeed be stretched by a factor related to the 8 in front of x, and translated based on the constants 84 and 5.
To correct the question, we would need to clarify the transformations properly. First is the stretch: If the function is y = 8∛(x - 84) - 5, then it is stretched by a factor of 8. The translation would be 84 units to the right (because of x - 84 within the cube root) and 5 units down (because of the - 5 at the end).