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: 6


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

Work Step by Step

We first see that our new graph is our old one shifted to the right by $2$ units because the initial graph has the zeros $0$ and $3$ and the new one has the zeros of $0 +2$ and $3 + 2$ which is $2$ and $5$. Therefore we subtract $2$ from the $x$ within $f(x)$ giving us: $y = \sqrt {3(x-2)-{(x-2)}^{2}}$ We then see that instead of having $y=1.5$ as the max in our function, our new function reaches $y = 3$. Since we know that $3 = 2(1.5)$, we know that our new graph is vertically stretched by 2. Therefore we must multiply our entire function by 2 giving us: $y = 2\sqrt {3(x-2)-{(x-2)}^{2}}$ as our final answer for the function of our new graph.
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