https://file.aiquickdraw.com/mathbot/file/1726846429709d45n7h9m.jpg

The graph in the image represents a "V"-shaped graph, which suggests it is the graph of an absolute value function. The function seems to have a vertex at \((-1, -1)\), and the slopes of the two linear parts are different on either side of the vertex. Let's break this down.

### Key observations:
1. **Vertex**: The point \((-1, -1)\) is the lowest point, indicating that this is the vertex of the function.
2. **Slope**:
   - On the left of \(x = -1\) (from \((-5, 3)\) to \((-1, -1)\)), the slope is \(\frac{-4}{4} = -1\).
   - On the right of \(x = -1\) (from \((-1, -1)\) to \((3, 3)\)), the slope is \(\frac{4}{4} = 1\).

### General form of an absolute value function:
\[
y = a|x - h| + k
\]
Where:
- \( (h, k) \) is the vertex, so \(h = -1\) and \(k = -1\).
- The slope \(a\) is determined by the rate of change on either side of the vertex. Here, \(a = 1\) since the slopes are \(1\) and \(-1\).

### Therefore, the equation of the function is:
\[
y = |x + 1| - 1
\]

Let me know if you need further clarification or details!

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Here are five questions that build on this:
1. What is the significance of the vertex in an absolute value function?
2. How would the graph shift if we changed the equation to \(y = |x + 2| - 1\)?
3. How does the slope change affect the shape of the graph?
4. What would the equation be if the vertex were located at \((-2, 3)\)?
5. How do you interpret the impact of the constant \(k\) in the absolute value function equation?

**Tip**: Always identify the vertex when working with absolute value functions—it helps set the foundation for the equation.

Complete an equation for the function graphed above.

Learn how to find the equation of an absolute value function with a graph. This problem involves identifying the vertex and slope of the function and constructing the equation using the formula y = a|x - h| + k. Suitable for students in Grades 8-10.

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