Question

Use the image to answer the question.

a coordinate plane for f of x versus x

Describe the behavior of the function by determining over which interval the function has a negative average rate of change. Consider only intervals with consecutive endpoints shown on the graph.

(1 point)
The average rate of change is negative over the interval [
,
].
Remaining Attempts : 3
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Answer 1

To determine the average rate of change of the function \( f(x) \) over an interval \([a, b]\), you can use the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

The average rate of change is negative when \( f(b) < f(a) \), meaning that the function is decreasing over that interval.

Since I cannot see an actual image of the graph on which the function is plotted, I can guide you on how to find the interval with a negative average rate of change:

1. Identify the coordinates of key points (consecutive endpoints) on the graph where you can apply the average rate of change formula.
2. Check the function values, \( f(a) \) and \( f(b) \), at these points.
3. Determine if the condition \( f(b) < f(a) \) holds for any chosen intervals.

If you provide the specific points or characteristics of the graph, I can assist you further in identifying the interval where the function has a negative average rate of change.