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The question is asking what transformations are needed to transform the graph of the cube root function \( f(x) = \sqrt[3]{x} \) into the function \( h(x) = -\sqrt[3]{x - 4} \).

Let's break down the transformation of \( f(x) = \sqrt[3]{x} \) to \( h(x) = -\sqrt[3]{x - 4} \):

1. **Horizontal Shift**: 
   The term \( x - 4 \) inside the cube root means the function is shifted **horizontally to the right** by 4 units. In general, \( \sqrt[3]{x - h} \) shifts the graph to the right by \( h \) units.

2. **Reflection**: 
   The negative sign in front of the cube root function, \( -\sqrt[3]{x - 4} \), reflects the graph across the x-axis. A negative outside the function indicates reflection over the x-axis.

Thus, the graph of \( f(x) = \sqrt[3]{x} \) should be:
- Horizontally shifted **4 units to the right**, and
- Reflected across the **x-axis**.

The correct answer is **A**: "The graph of \( f(x) = \sqrt[3]{x} \) should be horizontally shifted to the right by 4 units and reflected about the x-axis."

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Would you like more details or have any questions?

Here are 5 related questions:
1. What other types of transformations can be applied to the cube root function?
2. How do you graph a vertical stretch or compression?
3. What happens if the negative sign is inside the cube root function?
4. How would a vertical shift affect the transformation of this graph?
5. Can this method be applied to functions other than cube root functions?

**Tip**: Always identify shifts, reflections, and stretches/compressions by analyzing changes both inside and outside the function.

What transformations are needed to graph the function h(x) = -³√(x - 4)? Choose the correct answer below.

Learn how to transform the cube root function f(x) = ³√x to h(x) = -³√(x - 4) by shifting the graph 4 units to the right and reflecting it across the x-axis. Suitable for high school students studying function transformations.

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