Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.3 - New Functions from Old Functions - 1.3 Exercises - Page 43: 18

Answer

Parent function: $y=cosx$ Transformations: 1) $y=2cosx$ 2) $y=-2cosx$ 3) $y=-2cosx+3$ See image.

Work Step by Step

To graph the function, let's take the parent function and start transformations on it. (1) Graph the parent function $y=cosx$ (Blue line graph). (2) Graph $y=2cosx$ by stretching the parent function vertically by a factor of 2 (Blue dotted line graph). (3) Graph $y=-2cosx$ by reflecting the previous graph about the $x$-axis (Red dotted line graph) (4) Graph $y=-2cosx+3$ by shifting the previous graph by 3 units upward (Red line graph).
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