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In this problem, we are given two graphs, one for \( f(x) \) (the blue curve) and one for \( g(x) \) (the red curve). We are asked to find the formula for \( g(x) \) in terms of \( f(x) \).

### Observations:
- The graph of \( f(x) \) appears to be a cubic or higher-degree function based on its oscillating nature.
- The graph of \( g(x) \) appears to resemble a horizontally shifted version of \( f(x) \).

### Hypothesis:
By visually comparing the graphs, it looks like \( g(x) \) is a **horizontal shift** of \( f(x) \). More specifically:
- The local maximum and minimum points of \( f(x) \) seem to shift to the right in \( g(x) \).
- Therefore, the transformation might be of the form:
  \[
  g(x) = f(x - c)
  \]
  where \( c \) is the horizontal shift.

### Estimating the Shift:
From the graphs:
- \( f(x) \) has a local minimum around \( x = -2 \) and \( x = 1 \).
- \( g(x) \) has its corresponding minimum at \( x = 0 \) and \( x = 3 \), indicating a shift of approximately \( +2 \) units.

Thus, a likely formula for \( g(x) \) in terms of \( f(x) \) is:
\[
g(x) = f(x - 2)
\]

Would you like to explore this further or check specific points to verify? 

### Related Questions:
1. How does a horizontal shift affect the graph of a function?
2. What are the key differences between vertical and horizontal shifts?
3. Can we generalize this shift to any function \( f(x) \)?
4. What happens to the domain and range of a function after a horizontal shift?
5. Can you express other transformations, such as reflections or dilations, similarly?

**Tip:** For horizontal shifts, remember that shifting right corresponds to subtracting from \( x \), while shifting left corresponds to adding to \( x \).

Learn how to express g(x) as a horizontal shift of f(x) by analyzing their graphs. This problem explores function transformations and how shifts affect a function's graph. Suitable for students in Grades 10-12.

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