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The problem involves finding the correct transformation of the function \( f(x) \) to obtain \( g(x) \).

### Analyzing the Graphs:
1. **Original Function \( f(x) \)**:
   - The orange curve represents \( f(x) \).
   - This is a rational function with vertical and horizontal asymptotes at \( x = 0 \) and \( y = 0 \), respectively.

2. **Transformed Function \( g(x) \)**:
   - The blue curve represents \( g(x) \).
   - Notice that \( g(x) \) is a reflection of \( f(x) \) about the x-axis, which implies a transformation of \( f(x) \) to \( -f(x) \).

3. **Horizontal Translation**:
   - The graph of \( g(x) \) appears to be shifted to the right by 2 units when compared to \( f(x) \). 
   - A horizontal shift to the right is represented by replacing \( x \) with \( (x - 2) \) in the function.

### Conclusion:
Given that \( g(x) \) is obtained by reflecting \( f(x) \) over the x-axis and then shifting it to the right by 2 units, the correct expression for \( g(x) \) in terms of \( f(x) \) is:
\[
g(x) = -f(x - 2)
\]
However, it seems the incorrect answer was selected as \( g(x) = -f(x) + 2 \) on the provided options.

Would you like more details or have any questions?

Here are some related questions for further practice:
1. What effect does shifting a function to the left have on its equation?
2. How does reflecting a function over the y-axis change its equation?
3. If a function is reflected over the x-axis and then shifted up, how would its equation change?
4. How do horizontal shifts affect the domain of a function?
5. What transformations would you apply to obtain the equation \( g(x) = f(-x + 3) \) from \( f(x) \)?

**Tip**: Always remember that a horizontal shift to the right is represented by subtracting from the \( x \)-value, while a shift to the left is represented by adding to the \( x \)-value.

Function f undergoes two transformations to become g. Express g(x) in terms of f(x).

Understand how to apply transformations to a function by reflecting it over the x-axis and shifting it horizontally. Learn how g(x) is obtained from f(x) through transformations in this detailed example.

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