Question

describe the behavior of the function by determining which intervals the function has a positivr average rate of change
graph= starts at 0 goes up to 5,5 goes down to 3,8 goes up to 10,15

Answer 1

To analyze the behavior of the function you described based on its graph, we will break it down into its segments. The function appears to have distinct intervals where it increases or decreases:

1. **From 0 to 5**: The function starts at 0 and increases steadily to 5. Since the function is going up, it has a positive average rate of change in this interval.

2. **From 5 to 8**: The function decreases from 5 to 3. This means that the average rate of change is negative during this interval.

3. **From 8 to 10**: The function increases again from 3 to 15. In this segment, since the function is increasing, it has a positive average rate of change.

Now, summarizing the intervals:

- The function has a **positive average rate of change** in the intervals:
- \( (0, 5) \)
- \( (8, 15) \)

- The function has a **negative average rate of change** in the interval:
- \( (5, 8) \)

This breakdown illustrates where the function is increasing or decreasing based on the provided description.