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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.4: Logarithmic Functions
Problem 45E
Related questions
Question
1. Sketch the graphs of the two functions f : [0, π] → R, g : [0, π] → R where
f(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
f(x) =
−1 x ∈ (−∞, −3)
2x
3 + 2 −3 ≤ x ≤ 0
√
4 − x
2 x ∈ (0, 2)
x
2 − 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) to
your picture.
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