To determine the intervals on which the function is increasing based on the provided description, let’s analyze the behavior of the function:
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From left to right: The function starts at infinity, approaches a cusp at \((-1, 0)\), which suggests a vertical tangent or a point where the slope changes direction, indicating the function is decreasing until it reaches this point.
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From the cusp at \((-1, 0)\) to the local maximum at \((0, 1)\): The function rises from the cusp, suggesting that it is increasing on the interval \((-1, 0)\).
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From the local maximum at \((0, 1)\) to the cusp at \((1, 0)\): The function decreases from the maximum at \((0, 1)\) to the cusp at \((1, 0)\), indicating it is not increasing in this interval.
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From the cusp at \((1, 0)\) to infinity: The function is rising again after this cusp, suggesting it is increasing on the interval \((1, \infty)\).
Combining the intervals where the function is increasing, we get \((-1, 0)\) and \((1, \infty)\).
Thus, the correct answer to the question about on which interval the function is increasing is:
left-parenthesis negative 1 comma 1 right-parenthesis union left-parenthesis 1 comma infinity right-parenthesis.
1 answer