Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 104: 53


See graph

Work Step by Step

We are given the function: $g(x)=2\sqrt{x-2}+1$ We start graphing with the basic function $a(x)=\sqrt x$. We horizontally shift $a(x)$ by 2 units to the right to get $b(x)=\sqrt{x-2}$. Then we vertically stretch $b(x)$ by a factor of 2 to get $c(x)=2\sqrt{x-2}$. Finally we vertically shift $c(x)$ one unit upward to get $g(x)=2\sqrt{x-2}+1$. We use 3 points: $(2,1),(3,3),(6,5)$.
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