https://file.aiquickdraw.com/mathbot/file/1726676839578bvq7wbip.jpg

The problem gives us the point \( A(-3, 2) \) on the graph of \( y = f(x) \) and asks for the image of \( A \) when the graph is transformed to \( y = -f(x) + 3 \).

### Step-by-step approach:

1. **Given Information**:
   - \( A(-3, 2) \) lies on the graph of \( y = f(x) \), meaning \( f(-3) = 2 \).

2. **Transformation**:
   The transformation is \( y = -f(x) + 3 \).
   - The term \( -f(x) \) reflects the graph over the x-axis.
   - The term \( +3 \) shifts the graph vertically by 3 units upwards.

3. **Apply the transformation to the point**:
   - Start with \( f(-3) = 2 \).
   - For the new function, \( y = -f(x) + 3 \):
     \[
     y = -f(-3) + 3 = -(2) + 3 = -2 + 3 = 1
     \]

Thus, the image of point \( A(-3, 2) \) under the transformation is \( (-3, 1) \).

### Conclusion:
The image of \( A \) will be \( (-3, 1) \).

Let me know if you'd like further details or have any questions!

### Related questions:
1. What is the effect of the transformation \( y = -f(x) \) on the graph?
2. How does a vertical shift affect the coordinates of a point on a graph?
3. What happens to the graph when a negative sign is applied to a function?
4. How can we generalize transformations for any point \( (x_1, y_1) \)?
5. Can you explain what a horizontal reflection would look like?

### Tip:
Whenever dealing with transformations, always consider how the reflection (negative sign) and shifts affect each point individually.

The point A(-3, 2) lies on the graph with equation y = f(x). If the graph of the related function y = -f(x) + 3 is drawn, what will the image of A be?

Understand how to transform the function y = f(x) by reflecting it and applying a vertical shift. This example uses point A(-3, 2) on the graph of y = f(x) to determine the new image after the transformation y = -f(x) + 3.

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