To accurately describe the graph of \( f(x) \) based on the average rate of change that is indicated for different intervals, one needs to analyze how \( f(x) \) behaves on those intervals.
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The average rate of change of a function \( f \) on an interval \([a, b]\) can be calculated using the formula: \[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \] If this value is negative, it indicates that the function \( f(x) \) is decreasing over that interval.
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Based on the responses you provided, you would choose the statements that indicate where the average rate of change is negative.
Without the specific graph or function provided, it's difficult to definitively select the correct response. However, here's how you would analyze it:
- If you see that the function goes down from left to right between specific x-values, then you'd take that interval as a negative rate of change.
- If there are multiple intervals where the function decreases, you would indicate all such intervals.
If you have specific graphical information, here's how to interpret it:
- If the graph shows a decline in \( f(x) \) between points \( 0 \) to \( 1 \) and \( 3 \) to \( 4 \), then you would choose the first statement.
- If it declines only between \( 6 \) to \( 7 \), pick the second option.
- And so on for each option.
Conclusion:
You should analyze the graph or table of values for \( f(x) \) to assess which intervals exhibit a negative average rate of change and then select the appropriate option based on your observations. If the graph is not visible in your context, it would be impossible to identify the exact intervals purely based on the descriptions provided.
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