The <em><u>correct answer</u></em> is:
Compared to the parent graph, this graph is compressed horizontally, reflected across the y-axis, and shifted right 4 units.
Explanation:
The parent function in this situation is .
Algebraically, the changes we can see from the parent function to this function is that the variable is multiplied by 8, negated, and had 4 subtracted from it.
When we negate the variable, this reflects the graph across the y-axis.
When we multiply the variable by a number greater than 1, this horizontally compresses the graph.
When we subtract a number from the variable before taking the cubed root, this shifts the graph horizontally; specifically, it shifts it to the right.
Thus the graph will be reflected across the y-axis, horizontally compressed by 1/8, and shifted 4 units to the right.
