To determine the interval over which the function has a negative average rate of change, we need to look for an interval where the function's value decreases as the input increases.
- If the function is decreasing (the graph slopes downwards), then the average rate of change over that interval will be negative.
- If the function is increasing (the graph slopes upwards), then the average rate of change will be positive.
Based on the options given, we can analyze the intervals:
- [1, 2]: Check the values at x = 1 and x = 2. If the value at x = 2 is less than the value at x = 1, it indicates a negative average rate of change.
- [0, 1]: Similar evaluation would apply here.
- [3, 5]: Check the values at x = 3 and x = 5.
- [2, 3]: Check at x = 2 and x = 3.
Without the image for reference, I can't determine which of those intervals is where the function has a negative average rate of change. However, you can visually assess the function over those intervals to find where it is decreasing.
Once you find the interval where the function's output is decreasing as x increases, that will be your answer for the negative average rate of change.
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