To analyze the graph of \( f(x) \), you need to look at the sections of the graph where the function decreases. The average rate of change on an interval \([a, b]\) can be determined by finding the change in the function values:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
If \( f(b) < f(a) \), the average rate of change is negative.
Based on typical interpretations of a graph:
- Check the interval \([1, 3]\): If the graph is going downward between \( x = 1 \) and \( x = 3\), then the average rate of change is negative in this interval.
- Check the interval \([6, 7]\): Similarly, see if the graph is descending between these points.
- Look at the intervals \([0, 1]\) and \([3, 4]\) for any downward trends.
After evaluating these intervals based on the graph, you would select the appropriate statement.
If the average rate of change is negative for both \([1,3]\) and \([6,7]\), then the correct response would be:
"The average rate of change is negative on the interval \([1, 3]\) and also on the interval \([6, 7]\)."
If it's negative only in one of those intervals, pick the corresponding statement. Finally, if there's negativity in intervals like \([0,1]\) and \([3,4]\), you would choose that response instead.
Without seeing the specific graph, I cannot definitively choose which statement to select. Please analyze the graph according to these guidelines to identify the correct statement.
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