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: 7

Answer

$y = -\sqrt {3(x+4) - {(x+4)}^{2}} -1$

Work Step by Step

The first thing we see is that the two points we initially had along the x-axis have been shifted to the left by 4 units ($0 - 4 = -4$ and $3-4 = -1$). Therefore we must add 4 to the x inside our original function. $y = \sqrt {3(x+4) - {(x+4)}^{2}}$ Then since our graph has been flipped so that the curve faces upwards now instead of downwards, we know that there has been a reflection over the x-axis so we must multiply our entire function by $-1$ giving us: $y = -\sqrt {3(x+4) - {(x+4)}^{2}}$ Lastly, we can clearly see that our function has been shifted downwards by 1 as the two points that were initially touching the x-axis now have the y-values of $-1$. Therefore we must subtract $1$ from the end of our function. This gives us; $y = -\sqrt {3(x+4) - {(x+4)}^{2}} -1$ as our final answer.
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