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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.

Use transformations of the graph of f(x) = x^3 to determine the graph of the given function. g(x) = (x + 3)^3. Select all the transformations that are needed to graph the given function using f(x) = x^3.

Understand how to apply transformations to the graph of a cubic function. Learn how to shift the graph of f(x) = x^3 to obtain g(x) = (x + 3)^3, including horizontal shifts to the left. Suitable for high school students studying graph transformations.

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