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!

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.