Without having the image of the graph, I'm unable to provide a direct answer based on visual analysis. However, I can help explain how to determine the average rate of change on any given interval.
To find the average rate of change of a function \( f(x) \) over an interval \([a, b]\), you would use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
From here, you can assess the slope:
- If the result is positive, the average rate of change is positive (the graph is increasing).
- If the result is negative, the average rate of change is negative (the graph is decreasing).
- If the result is zero, there is no change (the graph is constant).
To choose the correct statement among the options you've provided, you would need to evaluate the function \( f \) at the described intervals:
- Check the values of \( f(1) \) and \( f(3) \) for the interval \([1, 3]\).
- Check the values of \( f(6) \) and \( f(7) \) for the interval \([6, 7]\).
- Check the values of \( f(0) \) and \( f(1) \) for the interval \([0, 1]\).
- Check the values of \( f(3) \) and \( f(4) \) for the interval \([3, 4]\).
Once you have these values, you can determine whether the average rate of change for each interval is negative, positive, or zero and select the appropriate response based on your findings.
If you can describe the graph or provide specific points, I'd be happy to assist further with that information!
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