https://file.aiquickdraw.com/mathbot/file/1726400408623dmqdz2ne.jpg

The task asks you to sketch the graph of \( y = f(x) + 2 \) based on the graph of \( y = f(x) \) and to label the coordinates of the maximum point.

### Steps to solve:

1. **Effect of \( +2 \) on the graph**:
   - The term \( +2 \) indicates a vertical translation. Specifically, it means that the graph of \( y = f(x) \) is shifted 2 units upward. Every point on the graph will move 2 units higher than it was on \( y = f(x) \).
   
2. **Maximum point adjustment**:
   - If the maximum point of \( y = f(x) \) is at coordinates \( (x_{\text{max}}, y_{\text{max}}) \), then the maximum point of \( y = f(x) + 2 \) will be at \( (x_{\text{max}}, y_{\text{max}} + 2) \).

Since the graph of \( y = f(x) \) is not shown in the image, I would need the coordinates of its maximum point to give you the exact new maximum. If the maximum point is visible, you can simply add 2 to the \( y \)-coordinate of that point.

Would you like to describe the maximum point of the graph or share the graph of \( f(x) \)? Let me know if you need further assistance!

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### Related Questions:
1. What happens to the graph when you subtract 2 instead of adding 2?
2. How does the graph change if we apply \( f(x - 2) \) instead of \( f(x) + 2 \)?
3. What is the effect of multiplying \( f(x) \) by a constant (e.g., \( 2f(x) \))?
4. How would the graph shift if the transformation was \( f(x + 3) \)?
5. Can you describe how a horizontal stretch affects the graph of \( f(x) \)?

### Tip:
When dealing with vertical shifts, always focus on the change in the \( y \)-coordinate of key points, as the \( x \)-coordinates remain the same.

The graph of y = f(x) is shown to the right. Sketch the graph of y = f(x) + 2, labelling the coordinates of the maximum point.

Learn how to sketch the graph of y = f(x) + 2 from the given graph of y = f(x). Understand vertical shifts and transformations. Includes labeling of the maximum point. Suitable for students in Grades 9-12.

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