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The graph you have provided shows a piecewise function composed of different segments:

1. A horizontal line segment from \((-9, 1)\) to \((-5, 1)\), with closed endpoints.
2. An open point at \((-4, 1)\) and a curve that dips down to \((-2, 0)\), resembling a parabola, and then rises to \((0, 2)\).
3. A straight line segment starting from \((0, 2)\) and rising to \((1, 7)\) with an open point at \((1, 7)\).
4. A horizontal line segment starting from a closed point at \((1, 8)\) and continuing horizontally to \((6, 8)\) with an open point at \((6, 8)\).

Would you like further details on any of these sections, or an interpretation of the function based on this graph?

Here are five questions to expand your understanding:
1. What is the domain of this piecewise function?
2. What are the intervals where the function is increasing, decreasing, or constant?
3. How can you express this piecewise function algebraically?
4. What does the open and closed point notation indicate about the function at those points?
5. How would you describe the behavior of the function at \( x = -4 \), \( x = 1 \), and \( x = 6 \)?

**Tip:** When interpreting a graph, always check for open and closed points to determine whether the function includes or excludes the endpoints at those values.

Interpret the piecewise function graph shown.

This piecewise function graph involves horizontal and vertical segments, curves, and open/closed points, exploring function behavior over various intervals. Suitable for students in Grades 9-12, this problem emphasizes interpreting piecewise functions and understanding discontinuity points.

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