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], Multiple fill-in-the-blank
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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.
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],
Find the interval on which the function 𝑓 ( 𝑥 ) = 𝑥 ln 𝑥 is increasing.
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