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The problem involves identifying the transformation of a parent function based on the provided data.

1. **Parent Function**: The problem identifies the parent function as \( f(x) = x^3 \).
   
2. **Key Values of the Parent Function**: Below is the table for \( f(x) = x^3 \):
   - For \( x = -2 \), \( f(-2) = (-2)^3 = -8 \)
   - For \( x = -1 \), \( f(-1) = (-1)^3 = -1 \)
   - For \( x = 0 \), \( f(0) = 0^3 = 0 \)
   - For \( x = 1 \), \( f(1) = 1^3 = 1 \)
   - For \( x = 2 \), \( f(2) = 2^3 = 8 \)

   Thus, the values of the parent function should be:
   \[
   \begin{array}{|c|c|}
   \hline
   x & y = f(x) = x^3 \\
   \hline
   -2 & -8 \\
   -1 & -1 \\
   0 & 0 \\
   1 & 1 \\
   2 & 8 \\
   \hline
   \end{array}
   \]

3. **Transformation**:
   The transformation is described by comparing the given data points in the table (for the transformed function) and the parent function. Let's analyze the values:
   - When \( x = -10 \), the transformed \( y = -8 \)
   - When \( x = -5 \), the transformed \( y = -1 \)
   - When \( x = 0 \), the transformed \( y = 0 \)
   - When \( x = 5 \), the transformed \( y = 1 \)
   - When \( x = 10 \), the transformed \( y = 8 \)

   These values indicate that the transformed function is a horizontal stretch of the parent function. It appears to have been horizontally stretched by a factor of 5. This suggests the transformation is \( f(x) = \left( \frac{x}{5} \right)^3 \).

Would you like further details or explanations? 

Here are five related questions for deeper exploration:
1. How do you identify different transformations of a function (e.g., vertical/horizontal shifts and stretches)?
2. How can you generalize the transformation \( f(x) = a(x - h)^3 + k \) for any cubic function?
3. What other types of parent functions commonly undergo transformations, and how do their graphs change?
4. How does a horizontal stretch or compression affect the rate of change of the function?
5. How does the transformation of the function affect its symmetry properties?

**Tip**: When working with function transformations, always start by comparing key values and their respective shifts to determine the type of transformation (stretch, shift, reflection, etc.).

Identify the transformation from the parent function f(x) = x^3 based on the given data.

Analyze the transformation of the cubic parent function f(x) = x^3, using given data points to determine horizontal stretches and compressions. Learn how to compare the key values of the parent and transformed function to identify changes.

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