https://file.aiquickdraw.com/mathbot/file/1726927611547popr2f3a.jpg

The first graph represents the function \( f(x) \), and the second graph represents a transformation of \( f(x) \). By examining the graphs closely, we can determine how the second graph relates to the original function.

### Observations:
1. The basic shape of the graph has not changed, meaning no stretching, shrinking, or reflections are involved.
2. The second graph appears to be shifted **up** by 2 units. This can be seen by comparing the \( y \)-coordinates of corresponding points in both graphs.

### Conclusion:
The function represented by the second graph is \( f(x) + 2 \), which means the original function \( f(x) \) has been vertically translated upward by 2 units.

### Expression:
The function in terms of \( f(x) \) is:
\[
g(x) = f(x) + 2
\]

Would you like more details or have any questions about the transformations?

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Here are 5 related questions to deepen understanding:
1. What happens to the graph of \( f(x) \) if we shift it down by 3 units instead of up?
2. How would the graph change if we applied the transformation \( f(x - 1) \)?
3. What is the effect of reflecting the graph of \( f(x) \) over the \( x \)-axis?
4. Can you describe the transformation \( f(x) - 4 \) and how the graph would look?
5. How would the graph change if we apply a horizontal shift to the right by 2 units?

**Tip:** Vertical shifts affect only the \( y \)-coordinates of a graph, while horizontal shifts change the \( x \)-coordinates.

In terms of f(x), what is the function graphed below?

Learn about vertical shifts in functions through an example problem. The graph of f(x) is vertically shifted by 2 units. This solution covers function transformations and vertical translations, suitable for students in Grades 9-11.

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