Answer: stretched by a factor of 2 and translated 8 units right and 5 units down

Explanation:

These is the set of choices that accompany with this question:

a) stretched by a factor of 2 and translated 64 units right and 5 units down
b) stretched by a factor of 8 and translated 8 units right and 5 units down
c) stretched by a factor of 2 and translated 8 units right and 5 units down
d) stretched by a factor of 8 and translated 64 units right and 5 units down

Solution:
Let's work a little the given function to compare it with the parent function.
1) The given function is y = ?[8x - 64] - 5

2) Extract common factor 8 of the expression inside the square brackets:
y = ?[ 8( x - 8) ] - 5

3) Extract 8 from the root:
y = 2?(x - 8) - 5

4) The parent function is ?x. Call the parent function g(x) => g(x) = ?x

5) Compare: y is 2 * g(x - 8) - 5

6) Analyze the meaning of that:

g(x - 8) means that the graph of the function is translated 8 units to the right

scaling by 2 means that the graph is stretch vertically (by a scale factor of 2)

- 5 means that the entire graph is shifted 5 units downward.

So, the description of the graph y = ?(8x - 64) - 5 compared to the parent cube root function is: stretched by a factor of 2 and translated 8 units right and 5 units down