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The problem presented is related to transformations of functions. It shows two graphs: one for \( f(x) \) in blue and the other for \( g(x) \) in red. The goal is to determine the relationship or transformation that maps \( f(x) \) to \( g(x) \).

### Steps to Analyze:
1. **Identify any vertical shifts**: Check if the red graph \( g(x) \) has been moved up or down compared to \( f(x) \).
2. **Check for horizontal shifts**: See if \( g(x) \) has been shifted left or right compared to \( f(x) \).
3. **Analyze reflections**: Check if \( g(x) \) is a reflection of \( f(x) \) about the x-axis or y-axis.
4. **Look for scaling**: Compare the stretching or compressing of the graph vertically or horizontally.
5. **Any combinations of the above transformations**.

### Based on the visual cues in the graphs:
- It appears that the graph of \( g(x) \) is a **horizontal reflection** of \( f(x) \), meaning that \( g(x) \) could be \( f(-x) \).
- This hypothesis suggests that the transformation applied is a reflection across the y-axis.

Thus, the formula for \( g(x) \) in terms of \( f(x) \) might be:
\[
g(x) = f(-x)
\]

Would you like more details about transformations, or do you have any other questions?

Here are 5 related questions to expand understanding:
1. How can vertical and horizontal shifts affect the formula of a function?
2. What does reflecting a function across the x-axis look like mathematically?
3. How do vertical and horizontal stretches and compressions modify the function’s graph?
4. How do you identify transformations by looking at two function graphs?
5. What is the effect of combining multiple transformations like shifts and reflections?

**Tip**: Always check the key points on the graphs (like intercepts and peaks) to help identify specific transformations.

Find the formula for g in terms of f. g(x) = ?

This problem explores how to determine g(x) in terms of f(x) by applying function transformations. Learn to identify horizontal reflections and other transformations through graph analysis. Suitable for high school students in Grades 10-12.

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