Here is the plot for the function \( f\left( \frac{x}{2} - 4 \right) \) along with its even and odd parts:

- **Blue Solid Line**: Represents the transformed function \( f\left( \frac{x}{2} - 4 \right) \).
- **Green Dashed Line**: Represents the even part of the transformed function.
- **Red Dashed Line**: Represents the odd part of the transformed function.

The transformed function shows a shift to the right and a horizontal scaling by a factor of 2, as expected. The even and odd parts decompose the function into its symmetrical components.

Would you like further details or explanations on this transformation or the calculation of the even and odd parts?

#### Related Questions:

1. How would the graph change if the transformation was \( f(2x - 4) \) instead?
2. What happens to the even and odd parts if we apply a vertical shift instead of a horizontal shift?
3. Can you derive a general formula for the even and odd parts of a linearly transformed function?
4. How does scaling affect the domain and range of the original function \(f(x)\)?
5. What are some real-world applications of decomposing functions into even and odd parts?

#### Tip:

When dealing with function transformations, always consider the sequence of transformations (scaling, shifting, reflecting) and their effects on the function’s graph.

Explore the graph transformation of f((x/2) - 4) and its even and odd parts. This detailed analysis covers the shift to the right and horizontal scaling by a factor of 2. Understand how the even and odd parts decompose the function into symmetrical components. Ideal for advanced high school students studying function transformations.

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