题目

MATH136-12P-IO-202510-I-81X M04: Midterm Exam Review Quiz - Timed

多项填空题

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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思路分析

We are asked to state where the function is increasing and where it is decreasing, using interval notation with inf for infinity. First, examine the options in the context of typical turning points: if a function has a critical point at x = 3, a common behavior is that the function increases to the right of 3 and decreases to the left of 3. This would give increasing on (3, ∞) and decreasing on (−∞, 3). Now evaluate each option for the Increasing blank: - (3, inf): This matches the idea that the function increases for all x greater than 3. It excludes 3 itself (which is typical if 3 is a critical point where the slope may be zero or undefined) and includes all larger x values. This is a valid increasing interval if the funct......Login to view full explanation

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类似问题

Given a function whose graph is shown below, under which interval/s is the graph increasing? A. ( − 3 , − 1 ) ∪ ( 2 , 4 ) B. ( − 1 , + ∞ ) C. ( − 3 , 1 ) D. ( − ∞ , − 3 ) ∪ ( − 1 , 2 ) ∪ ( 4 , + ∞ )

For 𝑓 and 𝑔 real valued functions defined for all real numbers, ( 𝑔 ∘ 𝑓 ) ( 𝑥 ) = 𝑔 ( 𝑓 ( 𝑥 ) ) or all 𝑥 . Which of the following is (are) true? I. If 𝑓 is increasing and 𝑔 is increasing, then 𝑔 ∘ 𝑓 is increasing. II. If 𝑓 is increasing and 𝑔 is decreasing, then 𝑔 ∘ 𝑓 is decreasing. III. If 𝑓 is decreasing and 𝑔 is increasing, then 𝑔 ∘ 𝑓 is decreasing.