To sketch the graph of $y = f(x+3) + 2$, let's break it down into transformations of the basic function $y = f(x)$:

1. Horizontal Shift:

   • The term $(x+3)$ inside the function represents a horizontal shift to the left by 3 units. This means every point on the graph of $y = f(x)$ moves 3 units to the left.

2. Vertical Shift:

   • The term $+2$ outside the function represents a vertical shift upwards by 2 units. This means every point on the graph of $y = f(x+3)$ moves 2 units upward.

Steps to Sketch:

• Start with the graph of the original function $y = f(x)$.
• Shift the graph 3 units to the left to account for $(x+3)$.
• Then, move the entire graph 2 units upward to account for the $+2$.

If the original graph of $y = f(x)$ is known, these steps can be directly applied to modify it.

Do you want to go through a specific example, or have any clarifications?

Questions:

1. What is the shape of the original function $f(x)$?
2. Can you describe a basic graph of $f(x)$ so I can help sketch the transformation?
3. Are there any key points or intercepts of $f(x)$ you'd like to adjust?
4. How does the graph change with other types of transformations (reflections, stretches)?
5. Do you need help sketching the graph step by step?

Tip: Always apply horizontal transformations (inside the function) before vertical transformations (outside).