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The problem asks you to express the transformation of the function \( f(x) \) in function notation, given the following steps:

1. **Reflection over the x-axis:** This changes the function \( f(x) \) to \( -f(x) \).
2. **Vertical stretch by a factor of 2:** After reflecting, this transformation scales the function by 2, resulting in \( -2f(x) \).
3. **Horizontal shift 3 units to the right:** This shifts the function to the right, changing the input by subtracting 3 from \( x \), which results in \( -2f(x - 3) \).

Thus, the function \( g(x) \), after applying all the transformations to \( f(x) \), is:

\[
g(x) = -2f(x - 3)
\]

Would you like a more detailed explanation or have any questions about these transformations?

Here are 5 related questions:
1. How would the transformation change if the function was shifted left instead of right?
2. What happens if the function is stretched horizontally instead of vertically?
3. How do transformations combine when more than one type is applied to a function?
4. How does a vertical reflection differ from a horizontal reflection in function notation?
5. What would the function look like if there was a vertical shift instead of a horizontal one?

**Tip:** Always apply transformations in the correct order: reflections, stretches/compressions, and then shifts!

A function f(x) is reflected over the x-axis and stretched vertically by a factor of 2, followed by a horizontal shift 3 units to the right, resulting in function g(x). Express this transformation of f(x) in function notation.

Learn how to transform a function by reflecting it over the x-axis, stretching it vertically, and shifting it horizontally. This problem involves expressing the transformation of f(x) into g(x) using correct function notation.

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