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Question

A coordinate plane for f of x versus x. the points are: -1, curves up a bit to 1, then curves down to a spot under 2 then curves up twice to a spot above 3 then continues to a spot over 5.

Describe the behavior of the function by determining over which interval the function has a negative average rate of change.

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

To determine where the function has a negative average rate of change, we need to identify intervals where the function is decreasing.

Based on your description, the function starts at \( f(-1) \) and curves up to \( f(1) \), then curves down to a point below \( f(2) \). This indicates a decrease. The function then curves up twice to a value above \( f(3) \) before continuing to a point over \( f(5) \).

Given this behavior, we can observe the following:

• The function is decreasing between the points \( f(1) \) (curving up) and \( f(2) \) (where it curves down).

Hence, the average rate of change is negative over the interval \([1, 2]\).

So, the answer is: The average rate of change is negative over the interval \([1, 2]\).