To determine where the function has a negative average rate of change, you would look for intervals where the function decreases. The average rate of change of a function \(f(x)\) over an interval \([a, b]\) can be found using the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
A negative average rate of change occurs when \(f(b) < f(a)\), meaning the function's value is decreasing as \(x\) moves from \(a\) to \(b\).
Since I cannot see the image you mentioned, I can’t provide specific values for the interval where the function's average rate of change is negative. To find the regions where this occurs:
- Identify any intervals on the graph where the function is sloping downwards (decreasing).
- Determine the endpoints of these intervals, which are the \(x\)-values at the beginning and end of the decreasing behavior.
Once you have identified this interval, you can fill in the blanks:
The average rate of change is negative over the interval \([a, b]\), where \(a\) and \(b\) are the specific x-values you identified from the graph.
If you provide specific details or characteristics from the graph, I can help further to specify the correct interval.
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