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).

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!