The problem asks you to determine the transformations needed to graph the function $g(x) = (x + 3)^3$ based on the parent function $f(x) = x^3$.

Step-by-step Explanation:

1. Parent Function: The parent function is $f(x) = x^3$, a cubic function.
2. Given Function: The transformed function is $g(x) = (x + 3)^3$.

Analyzing the Transformation:

• The given function has the form $g(x) = (x + 3)^3$.
• The $+ 3$ inside the parentheses indicates a horizontal shift to the left by 3 units.

The correct transformation is shift 3 units to the left. There are no vertical stretches, shrinks, or reflections involved here.

Correct Answer:

• H. Shift the graph 3 units to the left.

Would you like more details or have any questions?

Here are five related questions you might find useful:

1. How do horizontal shifts affect cubic functions graphically?
2. What happens if the transformation was $g(x) = (x - 3)^3$?
3. How would adding a constant outside the cube function $g(x) = x^3 + 3$ change the graph?
4. Can vertical stretches and shrinks apply to a cubic function, and how?
5. What would happen to the graph if there was a negative sign inside or outside the cube?

Tip: For any function, shifting left or right comes from changes inside the parentheses with $x$, while shifts up or down come from constants added outside.