To describe the continuity or discontinuity of the graphed function, we need to analyze the information given about the rays and isolated points.
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First Ray: This ray increases and includes the endpoint at \((-1, 2.5)\) but has a hole at \((-2, 2)\). This means that as you approach \((-2, 2)\) from the left on the first ray, the function approaches \(2\), but it is not defined at that point (hole). Therefore, there is a point of discontinuity at \((-2, 2)\).
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Isolated Point: There is a single point graphed at \((-2, 1)\). This point does not affect the continuity of the function at \((-2, 2)\) since the function was originally discontinuous at that location. The isolated point does not connect with the rays, further emphasizing that the function is not continuous at \(x = -2\).
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Second Ray: The second ray starts at an open point at \((-1, 3)\) and decreases to infinity. The openness at \((-1, 3)\) indicates another point of discontinuity at \((-1, 3)\) since the function does not actually attain this value at \(x = -1\). It transitions from the first ray to this open point, suggesting a jump discontinuity.
Summary:
- There is a discontinuity at \((-2, 2)\) due to the hole.
- There is another discontinuity at \((-1, 3)\) due to the open point.
- The function is generally discontinuous at these points, and while it is continuous on the intervals outside these points, the specified points cause overall discontinuity in the function.
Overall conclusion: The graphed function has points of discontinuity at \((-2, 2)\) and \((-1, 3)\), making the function discontinuous.