1. The problem asks to identify the parent cubic function and describe the transformation represented by the given function. 2. The parent cubic function is generally given by $$f(x) = x^3$$. 3. Horizontal translations shift the graph left or right by changing the input: $$f(x-h)$$ shifts right if $h>0$, left if $h<0$. 4. Vertical translations shift the graph up or down by adding or subtracting a constant: $$f(x) + k$$ shifts up if $k>0$, down if $k<0$. 5. Option A describes a horizontal translation 3 units left: $$f(x+3)$$. 6. Option B describes a vertical translation 3 units up: $$f(x) + 3$$. 7. Option C describes a horizontal translation 3 units right: $$f(x-3)$$. 8. Option D describes a vertical translation 3 units down: $$f(x) - 3$$. 9. Since the selected option is D, the parent function is $$f(x) = x^3$$ and the transformation is a vertical translation down by 3 units, represented by $$f(x) - 3 = x^3 - 3$$. Final answer: The parent function is the cubic function $$f(x) = x^3$$ and the transformation is a vertical translation 3 units down, $$f(x) - 3 = x^3 - 3$$.