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).

Learn how to sketch the graph of y = f(x+3) + 2 using function transformations. This tutorial breaks down the horizontal shift by 3 units to the left and vertical shift by 2 units upwards, making it perfect for students in Grades 10-12.

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