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The problem asks to describe the transformations for the function \( f(x) = -|x - 2| + 3 \). Let's break this down:

### Function: \( f(x) = -|x - 2| + 3 \)

1. **Start with the basic absolute value function: \( y = |x| \)**
   - This is a V-shaped graph with its vertex at the origin \((0,0)\).

2. **Horizontal shift (inside the absolute value): \( |x - 2| \)**
   - The function \( y = |x - 2| \) shifts the graph to the **right by 2 units**. 
   - The new vertex of the V-shape is now at \((2, 0)\).

3. **Vertical reflection (negative sign in front): \( -|x - 2| \)**
   - The negative sign reflects the graph **over the x-axis**. So, instead of opening upwards, the V-shape now opens downwards, creating an inverted V.

4. **Vertical shift (addition outside): \( -|x - 2| + 3 \)**
   - The graph is then shifted **up by 3 units**, moving the vertex from \((2, 0)\) to \((2, 3)\).

### Summary of Transformations:
1. Shift right by 2 units.
2. Reflect over the x-axis.
3. Shift up by 3 units.

Looking at the graph in your image, the inverted V-shape with its vertex at \((2,3)\) is consistent with these transformations.

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Would you like more details on any part of this explanation? Here are five related questions to further explore this concept:

1. How would the graph change if the transformation was \( f(x) = |x + 2| - 3 \)?
2. What would the effect of a vertical stretch or compression (e.g., \( f(x) = 2|x - 2| + 3 \)) be?
3. How can you algebraically find the vertex of an absolute value function like \( f(x) = |x - h| + k \)?
4. How do reflections and shifts affect the symmetry of a function?
5. How would you determine the domain and range of \( f(x) = -|x - 2| + 3 \)?

**Tip:** When analyzing transformations, always handle horizontal shifts (inside the function) before vertical shifts (outside).

Describe the transformations for the function f(x) = -|x - 2| + 3 based on the graph provided.

Understand the transformations applied to the absolute value function f(x) = -|x - 2| + 3. Learn how to describe the horizontal shift, reflection, and vertical shift involved in this transformation. Suitable for high school students in Grades 9-12.

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