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The problem asks you to write a function \( h(x) \) in terms of \( g(x) \), where \( h(x) \) is:

1. Flipped over the x-axis, and
2. Twice as wide as \( g(x) \).

### Solution:

1. **Flipping over the x-axis** means multiplying the function by \( -1 \). So, flipping \( g(x) \) would give \( -g(x) \).
2. **Twice as wide** means a horizontal stretch, which is done by replacing \( x \) with \( \frac{x}{2} \). This stretches the graph horizontally by a factor of 2.

Thus, the function \( h(x) \) is given by:
\[
h(x) = -g\left(\frac{x}{2}\right)
\]

This satisfies both the conditions of flipping over the x-axis and being twice as wide.

Would you like more details or have any further questions?

### Relative questions:
1. What happens to the graph of \( g(x) \) when it's flipped over the y-axis?
2. How would the function change if it was flipped over both the x-axis and the y-axis?
3. What effect does compressing a function by a factor of 2 have on its graph?
4. How does the transformation \( g(kx) \) affect the graph when \( k > 1 \) or \( 0 < k < 1 \)?
5. What happens to the domain and range of \( g(x) \) after these transformations?

### Tip:
When transforming functions, always check how horizontal and vertical stretches or reflections impact the graph, particularly on the domain and range.

Let g(x) be some function in the domain (-10, 10). Write a function h(x) in terms of g(x) which is identical to g(x), but is flipped over the x-axis, and is twice as wide as g(x).

Learn how to transform the function g(x) by flipping it over the x-axis and making it twice as wide. This problem involves reflections and horizontal stretches, suitable for students in Grades 9-12.

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