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MATH136-1IP-IO-202430-I-81X M04: Midterm Exam Review Quiz - Timed

Multiple fill-in-the-blank

State when the function is increasing and decreasing using interval notation.  Use inf for ∞\infty. Increasing: [Fill in the blank], Decreasing: [Fill in the blank],

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Question restatement: State when the function is increasing and decreasing using interval notation. Increasing: [Fill in the blank], Decreasing: [Fill in the blank]. Option analysis: - Option 1: '(-inf,-1)U(0,1)' This option uses the union symbol U to combine two intervals, suggesting the function increases on the left tail up to -1 and again from 0 to 1. If the intended correct pattern is two disjoint increasing pieces separated by a decreasing region, this could be plausible. The key check is whether the endpoints -1 and 0 are included or excluded; the given interval has open endpoints, which is typical if the derivative is zero at -1 and 0 or if those are critical points where increasing behavior changes. If the function indeed increases on (-inf, -1) and (0, 1) and is not increasing at -1, 0, this option correctly captures two increasing intervals with open endpoints. As presented, this is a plausible correct candidate for the increasing part. - Option 2: '(-inf,-1),(0,1)' This is essentially the same as Option 1 but uses a comma to separate the intervals instead of the union symbol. In standard interval notation, a comma between two interval expressions does not denote a union and c......Login to view full explanation

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