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The given question asks for the transformations needed to graph the function \( h(x) = \frac{1}{3} x^3 \) using the graph of \( f(x) = x^3 \).

Let’s break down the transformation rules step by step:

1. **Vertical Shrink**: The coefficient \( \frac{1}{3} \) in front of \( x^3 \) means the graph is vertically compressed by a factor of \( \frac{1}{3} \). This transformation makes the graph less steep. 
   
2. **No Horizontal Shifts or Stretches**: There is no transformation affecting the horizontal direction since the \( x^3 \) term is unchanged. 

### Now, reviewing the provided options:
- **Option B**: "Shrink the graph vertically by a factor of \( \frac{1}{3} \)" is **correct**.
  
None of the other options (horizontal shifts, stretches, or reflections) apply to this specific transformation.

### Final answer:
The only transformation needed is the vertical shrink by a factor of \( \frac{1}{3} \) (option B).

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Would you like more details or have any questions? Here are 5 follow-up questions related to graph transformations:

1. What is the effect of multiplying a function by a constant greater than 1?
2. How does a negative coefficient affect the graph of a function?
3. What is the difference between horizontal and vertical stretching?
4. How can you identify a vertical shift in a function?
5. How do you graph multiple transformations step by step?

**Tip**: Always consider the impact of each coefficient separately—look at vertical and horizontal changes independently when analyzing transformations!

Use transformations of the graph of f(x) = x^3 to determine the graph of h(x) = (1/3) * x^3.

Learn how to apply graph transformations to f(x) = x^3 to graph h(x) = (1/3) * x^3. The problem covers vertical shrink transformations and explains how the coefficient (1/3) compresses the graph vertically. Suitable for students in Grades 9-11.

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