The problem asks to sketch the graph of $y = f(x) + 2$ based on a given graph of $y = f(x)$, and label the coordinates of the maximum point.

The transformation $y = f(x) + 2$ is a vertical shift upwards by 2 units. So, every point on the original graph $y = f(x)$ will be shifted upwards by 2 units, including the maximum point.

Steps:

1. Identify the coordinates of the maximum point on the original graph $y = f(x)$.
2. Apply the transformation by adding 2 to the $y$-coordinate of the maximum point.
3. Sketch the new graph by shifting all points on $y = f(x)$ vertically by 2 units.
4. Label the coordinates of the new maximum point.

Please upload the graph or provide further information if you need a specific example or calculation of the maximum point. Would you like further details on how vertical shifts affect graphs?

Here are five related questions you might explore:

1. What effect does subtracting a constant have on the graph of $y = f(x)$?
2. How do horizontal shifts affect a graph?
3. Can you describe how $y = -f(x)$ transforms the graph of $y = f(x)$?
4. What happens if the transformation involves multiplying $f(x)$ by a constant?
5. How would a reflection over the $x$-axis impact the graph?

Tip: When transforming graphs, always adjust points systematically based on the transformation rule (up/down for vertical shifts, left/right for horizontal shifts).