https://file.aiquickdraw.com/mathbot/file/1729025904055xt9ihdcy.jpg

Let's analyze the graph to determine the correct function.

### Key Observations from the Graph:
1. **V-shape:** The graph suggests it is an **absolute value function**.
2. **Vertex at (-6, -3):** The V-shape’s point of reflection (the vertex) is located at **x = -6** and **y = -3**.
3. **Positive slope:** As we move right from the vertex, the slope is positive (1), indicating the function rises linearly from the vertex.
4. **Shifting:** The graph is shifted left by 6 units and down by 3 units.

### General Form of Absolute Value Functions:
- \( y = |x - h| + k \), where:
  - \( h \) shifts the graph horizontally.
  - \( k \) shifts it vertically.
  - If \( h \) is positive, the graph shifts left; if negative, it shifts right.
  
### Matching with the Answer Choices:
- From the observations, the function appears to be **shifted left by 6 units** and **down by 3 units**.
- This corresponds to:  
  \( y = |x + 6| - 3 \).

### Correct Answer:
- **A.** \( y = |x + 6| - 3 \).

Would you like further explanation, or do you have any additional questions?

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**5 Related Questions:**
1. What happens if we replace \( |x + 6| \) with \( |x - 6| \) in the function?
2. How do horizontal and vertical shifts affect absolute value graphs?
3. What is the difference between \( |x + 6| \) and \( |x - 6| \) graphically?
4. How can we determine the slope of an absolute value function?
5. How does changing the slope inside the absolute value (e.g., \( y = 2|x + 6| - 3 \)) modify the graph?

**Tip:**  
The vertex form of an absolute value function makes it easy to identify the vertex and any shifts directly from the equation!

Which of the following functions is graphed below?

This problem involves analyzing a graph of an absolute value function with horizontal and vertical shifts. The vertex of the function is at (-6, -3), leading to the equation y = |x + 6| - 3. Explore absolute value function transformations and learn how to identify the equation based on the graph.

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