Use the image to answer the question.

Question

A coordinate plane for f of x versus x. It starts from -1, goes up to 1, then drops back down to 3, then up to 5 and 6 and drops back down to 7

Describe the graph of f(x) by selecting the correct statement.

(1 point)
Responses

The average rate of change is negative on the interval [0,1] and on the interval [3,4].
The average rate of change is negative on the interval left bracket 0 comma 1 right bracket and on the interval left bracket 3 comma 4 right bracket .

The average rate of change is negative on the interval [1,3] and also on the interval [6,7].
The average rate of change is negative on the interval left bracket 1 comma 3 right bracket and also on the interval left bracket 6 comma 7 right bracket .

The average rate of change is negative only on the interval [1,3].
The average rate of change is negative only on the interval left bracket 1 comma 3 right bracket .

The average rate of change is negative only on the interval [6,7].
The average rate of change is negative only on the interval left bracket six comma seven right bracket .
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Answer 1

To determine the correct statement regarding the average rate of change of the function \( f(x) \) over the specified intervals, we analyze the behavior of the graph based on your description.

1. Interval [0,1]: The graph is increasing, so the average rate of change is positive.
2. Interval [1,3]: The graph drops from approximately 1 to 3, indicating that the average rate of change is negative.
3. Interval [3,4]: The graph increases from 3 to 5; hence the average rate of change is positive.
4. Interval [6,7]: The graph drops as it goes from approximately 6 to 7, indicating that the average rate of change is negative here as well.

Based on this analysis:

• The average rate of change is negative on the intervals [1,3] and [6,7].
• The average rate of change is not negative on the intervals [0,1] or [3,4].

Thus, the correct statement is:

The average rate of change is negative on the interval [1,3] and also on the interval [6,7].

This aligns with the responses you provided.