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.
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 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 piecewise function 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.
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
Expert Solution
Step 1
"Since you have asked multiple questions, we will solve the first question for you. If you want any specific
question to be solved, then please specify the question number or post only that question."
First we will sketch the graph of the function . Then, we will use the transformation to
