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The problem you provided involves determining the parent function for the given equation \( g(x) = -(-x)^3 - 9 \) and identifying the transformations applied.

Let's break it down step by step, according to the image and its selections:

1. **Parent Function:**
   The parent function of \( g(x) = -(-x)^3 - 9 \) is correctly chosen as **\( y = x^3 \)**, since the cubic form is preserved, but transformations are applied to it.

2. **Reflection:**
   Since we have \( -(-x)^3 \), the negative sign inside the cube impacts the graph, reflecting it across the y-axis, and the outer negative reflects it across the x-axis. Thus, the correct transformation is a **reflection across both axes**.

3. **Stretch/Compression:**
   There is no coefficient before the cubic term or any scaling factor that suggests a vertical stretch or compression. Hence, **no vertical stretch or compression** is applied.

4. **Vertical Shift:**
   The term \( -9 \) at the end of the function represents a vertical shift. The graph is shifted **down 9 units**, which is the correct selection.

5. **Horizontal Shift:**
   Since there is no horizontal translation term inside the parentheses with \( x \), there is **no horizontal shift**.

### Summary of Transformations:
- Reflection across both axes.
- No vertical stretch/compression.
- Vertical shift down by 9 units.
- No horizontal shift.

Would you like further clarification on any step, or details about specific transformations? 

Here are five related questions to expand your understanding:
1. How would the graph change if the reflection was only across one axis?
2. What if there was a coefficient like \( 2 \) multiplying \( (-x)^3 \)? How would that affect the stretch/compression?
3. How would a horizontal shift affect the overall transformation of the graph?
4. Can you explain why the vertical shift is downward rather than upward?
5. What would the transformation look like if the reflection was only applied to the y-axis?

**Tip:** When analyzing transformations, always check for signs inside and outside of the function for reflections and shifts.

Determine the parent function from which the graph of the function shown below can be obtained. Next, identify each transformation that can be applied to the parent function in order to obtain the graph of the function shown below: g(x) = -(-x)^3 - 9

Explore the detailed breakdown of transformations applied to the parent function y = x^3 to obtain the graph of g(x) = -(-x)^3 - 9. Learn about reflections across axes, vertical shifts, and other transformations suitable for Grades 10-12.

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