To determine the intervals over which a function has a negative average rate of change, we need to examine the function's behavior, particularly looking for sections where the function's value decreases as the input value increases.
The average rate of change of a function \( f(x) \) over the interval \([a, b]\) is calculated using the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
This rate will be negative if \( f(b) < f(a) \), indicating that the function decreases over the interval from \( a \) to \( b \).
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Identify endpoints: Look at the consecutive interval endpoints from the graph provided. These will likely include pairs such as \([x_1, x_2]\), \([x_2, x_3]\), etc.
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Determine function values: For each interval, evaluate \( f(a) \) and \( f(b) \) to see if \( f(b) < f(a) \).
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Identify intervals with negative average rate of change: Once negative changes are found, record those intervals.
Without specific data or a graph to analyze, I can't give you the exact intervals, but you would follow the steps above closely to analyze your own data.
Once you find the interval(s) with a negative average rate of change, you can complete the statement:
"The average rate of change is negative over the interval \([x_1, x_2]\)." Fill in \( x_1 \) and \( x_2 \) with the respective endpoints from your graph.