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: 7


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

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.