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: 16

Answer

Parent function: $y=sinx$ (the grey dotted line on the image) first transform to: $y=sin\pi x$ (the red line on the image) second transform to: $y=sin\pi x +1$ (which is the same as $y=1+sin\pi x$) (the blue line on the image)
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Work Step by Step

To graph the function $y=1+sin\pi x$, start by graphing the base (also called the parent), first we have to determine its parent function and graph it. Parent function will be $y=sinx$ (grey graph). First step will be to multiply $x$ by $\pi$ (shrinking the parent function horizontally by a factor of $\pi$), so we will get $y=sin\pi x$ (red graph). Now we have to add $1$ to this function and we will get $y=sin\pi x +1$ (shift the previous graph up by $1$ unit. (blue graph)).
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