To analyze the behavior of the function on the specified intervals, you need to visually inspect the graph of the function. However, since I can't see the graph, I can guide you on how to determine whether the function is increasing, decreasing, or constant on each interval.
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Increasing: The function is increasing on an interval if the graph moves upward as you move from left to right. This means for any two points in that interval, if \( x_1 < x_2 \), then \( f(x_1) < f(x_2) \).
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Decreasing: The function is decreasing on an interval if the graph moves downward as you move from left to right. This means for any two points in that interval, if \( x_1 < x_2 \), then \( f(x_1) > f(x_2) \).
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Constant: The function is constant on an interval if the graph is a flat line (horizontal) as you move from left to right. This means for any two points in that interval, \( f(x_1) = f(x_2) \).
Now, using this approach, look at each specified interval one by one:
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For \(1 < x < 2\): Check the graph and determine if the function is increasing, decreasing, or constant in this range.
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For \(2 < x < 5\): Inspect this interval and note the behavior of the function.
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For \(5 < x < 7\): Examine how the function behaves on this interval.
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For \(x > 7\): Look at the end behavior of the function in this domain.
Based on your observations from the graph, you can classify the behavior of the function accordingly. If you provide details about the graph's behavior in those intervals, I can help you classify them more specifically.
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