To determine the intervals over which the function has a negative average rate of change, we need to look at the behavior of the line segments specified in your graph.
- Based on your description, the line segments can be plotted between the points (1, 1), (1, 0), (1, 2), (-1, 3), and (1, 5).
Now, let's analyze the average rate of change for different intervals defined by these points:
- From (1, 1) to (1, 0): This segment is going down, so the average rate of change here is negative.
- From (1, 0) to (1, 2): This segment is going up, indicating a positive average rate of change.
- From (1, 2) to (-1, 3): This segment slopes downward if read from the origin to (1, 2) and then back to (-1, 3), which indicates a negative average rate of change for this interval as well.
- From (-1, 3) to (1, 5): This segment is also going up, indicating a positive average rate of change.
Putting it all together:
- The function has a negative average rate of change over the interval from (1, 1) to (1, 0).
- The function has a negative average rate of change also from (1,2) to (-1,3).
The average rate of change is negative over the interval [1, 0] and over the interval [1, -1]. (Note: The intervals should be actual ranges from one x value to another based on your points, so please adjust based on the context).
If you can provide the correct ranges, I can specify them correctly.
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