https://file.aiquickdraw.com/mathbot/file/1727289599923o7loz0ii.jpg

The graph you provided depicts a V-shaped function, indicating that it is an absolute value function. Now, let's analyze it step by step.

1. **Vertex of the absolute value function**: 
   - The vertex of the graph is at \( (2, -3) \), meaning the graph has been shifted horizontally 2 units to the right and vertically 3 units down.

2. **Basic form of the absolute value function**:
   - The general form of an absolute value function is \( y = |x - h| + k \), where \( (h, k) \) is the vertex. From the graph, we can identify that \( h = 2 \) and \( k = -3 \). 

3. **Shifts**:
   - The graph is shifted 2 units to the right, so the equation inside the absolute value should be \( |x - 2| \).
   - The graph is shifted 3 units down, so the vertical shift is \( -3 \).

4. **Final equation**: 
   - Combining these, the equation is \( y = |x - 2| - 3 \).

Now, let's match this with the given answer choices:

- **Option A**: \( y = |x - 2| + 3 \) (This is incorrect; the graph is shifted down, not up.)
- **Option B**: \( y = |x - 2| - 3 \) (This is correct.)
- **Option C**: \( y = |x + 2| - 3 \) (This is incorrect; the horizontal shift is wrong.)
- **Option D**: \( y = |x + 2| + 3 \) (This is incorrect; both the horizontal and vertical shifts are wrong.)

The correct answer is **B**.

Would you like further details on absolute value transformations or shifts? Here are some related questions to deepen your understanding:

1. What happens to the graph of an absolute value function when you change the sign inside the absolute value?
2. How do vertical shifts affect the graph of an absolute value function?
3. How would the graph change if the equation were \( y = -|x - 2| + 3 \)?
4. What is the slope of the lines forming the V-shape in this graph?
5. How would you determine the equation of an absolute value function if given only the graph?

**Tip**: The vertex of an absolute value function \( y = |x - h| + k \) always corresponds to the point \( (h, k) \), which makes it easy to identify shifts from the standard position.

Which equation represents the absolute value function shown in the graph?

Learn how to identify the equation of an absolute value function from its graph. The problem covers graph transformations, including horizontal and vertical shifts, and the general form of the absolute value function y = |x - h| + k. Suitable for students in Grades 8-10.

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