1. Sketch the graphs of the two functions f : [0, π] → R, g : [0, π] → R wheref(x) = sin(3x), and g(x) = 5 − 4 sin(3x).Explain carefully how you obtained the graph y = g(x) from the graph of y = f(x).(a) Write down the ranges of both f and g.(b) Is f one-one on this domain? Justify your answer.(c) Indicate an interval on the x–axis where f has an inverse. Justify your answer.(You have not been asked to find this inverse.)2. Sketch the graph of the following piecewise functionf(x) =−1 x ∈ (−∞, −3)2x3 + 2 −3 ≤ x ≤ 0√4 − x2 x ∈ (0, 2)x2 − 4 x ≥ 2.Let g(x) = −f(x) and h(x) = 1 − f(x). Add the sketches of y = g(x) and y = h(x) toyour picture.

1. Sketch the graphs of the two functions f : [0, π] → R, g : [0, π] → R wheref(x) = sin(3x), and g(x) = 5 − 4 sin(3x).Explain carefully how you obtained the graph y = g(x) from the graph of y = f(x).(a) Write down the ranges of both f and g.(b) Is f one-one on this domain? Justify your answer.(c) Indicate an interval on the x–axis where f has an inverse. Justify your answer.(You have not been asked to find this inverse.)2. Sketch the graph of the following piecewise functionf(x) =−1 x ∈ (−∞, −3)2x3 + 2 −3 ≤ x ≤ 0√4 − x2 x ∈ (0, 2)x2 − 4 x ≥ 2.Let g(x) = −f(x) and h(x) = 1 − f(x). Add the sketches of y = g(x) and y = h(x) toyour picture.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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