To determine which statement about the graph of \( f(x) \) is correct, we need to analyze the behavior of the function on the given intervals in terms of its average rate of change. The average rate of change of a function over an interval \([a, b]\) is calculated as:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
- If this value is negative, it means that the function is decreasing over that interval.
- If this value is positive, it means the function is increasing.
To select the correct statement, we would ideally need more information about the values of \( f(x) \) at those specific points. However, based on the statements provided, here’s how you could reason through them:
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The average rate of change is negative only on the interval [6, 7].
- This would mean \( f(7) < f(6) \) and no other intervals have a negative average rate of change.
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The average rate of change is negative on the interval [1, 3] and also on the interval [6, 7].
- This implies that \( f(3) < f(1) \) and \( f(7) < f(6) \).
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The average rate of change is negative on the interval [0, 1] and on the interval [3, 4].
- This indicates that \( f(1) < f(0) \) and \( f(4) < f(3) \).
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The average rate of change is negative only on the interval [1, 3].
- This means \( f(3) < f(1) \), but there are no negative slopes in any other intervals.
To find the correct answer, you would need to check the graph or the specific values of \( f(x) \) at each of the mentioned intervals. The statement that describes the correct behavior of the graph based on those intervals is the answer you need to select.
If you have access to the graph or values, you should look for periods where the function decreases across the intervals and confirm which statement accurately captures all of those intervals. If you're unable to analyze the graph or function right now, I recommend going with the option that seems most comprehensive based on your understanding.
1 answer