Hello from MrBillDoesMath!
Answer:
Choice A ("Four units to the left and 3 units down")
Discussion:
The parent function is y = x ^ (1/3) . Let's call y = (x +4) ^ (1/3) the "moved" function. When x = 0, the parent function = 0 but the "moved" function = 0 when x = -4. So the moved function is translated 4 units to the left of the parent function.
Also, when x = 0, the parent function = 0 but (x+4)^(1/3) -3 = 4^(1/3) = 3 = -1.4 (approx) so (x+4)^(1/3) -3 is translated downward or below the parent function.
Putting these facts together shows that Choice A ("Four units to the left and 3 units down") is the correct answer. This is verified in the attachment where the parent function is shown on "top" or above (x+4)^(1/3) -3.
Thank you,
MrB