To accurately answer your question about the graph of \( f(x) \), we would need to analyze the graph directly. However, since I can't view images or graphs, I can give you guidance on how to determine the average rate of change over various intervals based on general principles.
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Average Rate of Change: The average rate of change of a function \( f(x) \) over the interval \([a, b]\) can be calculated using the formula: \[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \] If \( f(b) < f(a) \), the average rate of change is negative on that interval.
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Interpreting the Intervals: You need to look at the values of \( f(x) \) at the endpoints of each interval:
- For \([0,1]\), compare \( f(1) \) and \( f(0) \).
- For \([1,3]\), compare \( f(3) \) and \( f(1) \).
- For \([3,4]\), compare \( f(4) \) and \( f(3) \).
- For \([6,7]\), compare \( f(7) \) and \( f(6) \).
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Making a Selection: After completing the comparisons, select the appropriate statement that matches the findings of your analysis.
Without the actual graph, I can't definitively choose the correct response, but follow these steps, and you should be able to identify the correct answer based on the observed trends. If you need more detailed help interpreting specific parts of the graph, feel free to describe it, and I can assist you further!