Question

Use the image to answer the question.

A coordinate plane for f of x versus x.

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

(1 point)
Responses

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 .

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 .
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Answer 1

To accurately determine the intervals where the average rate of change of the function \( f(x) \) is negative, you would typically analyze the graph of the function. The average rate of change of a function on an interval \([a, b]\) can be calculated using the formula:

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

If \( f(b) < f(a) \), then the average rate of change is negative on that interval.

Without seeing the graph, I cannot definitively tell you which statement is correct. However, you can look at the graph and identify:

1. Where the graph decreases, indicating a negative average rate of change.
2. Verify which of the proposed intervals show this behavior.

Please inspect the graph to see which intervals correspond to a negative average rate of change, and select the appropriate response based on that analysis.