Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 43: 8

Answer

a) The graph of $y=2\sin x$ is the graph of $y=\sin x$ stretched by a factor of 2 in the vertical direction. b) The graph of $y=1+\sqrt x $ is the graph of $y=\sqrt x$ shfted upwards 1 unit. The graph of both functions are shown in the attached answer_8.png file.
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Work Step by Step

a) The graph of $y=2\sin x$ is the graph of $y=\sin x$ stretched by a factor of 2 in the vertical direction because each y-coordinate of $y=\sin x$ is multiplied by 2. b) The graph of $y=1+\sqrt x $ is the graph of $y=\sqrt x$ shfted upwards 1 unit because each y-coordinate of the function $y=\sqrt x$ is increased by 1.
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