College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Section 2.7 - Graphing Techniques - 2.7 Exercises - Page 255: 22


See the picture below.

Work Step by Step

The parent function is $f(x)=\sqrt x$ (with red), but the graph of $g(x)=\sqrt{9x}$ which is equivalent to $g(x)=3\sqrt x$ (with blue) will be wider, as the coefficient multplies each y-value by 3. For drawing the exact graph of the parent function here is a table of values: $f(0)=\sqrt{ 0}=0$ $f(1)=\sqrt{1}=1$ $f(2)=\sqrt{2}$ $f(3)=\sqrt{3}$ $f(4)=\sqrt{4}=2$ By the use of graph transformation techniques, the graph is vertically stretched by a factor of $3$, as the coefficient is greater than 1. For drawing the exact graph of $g(x)$ here is the table of values of the given function: $g(0)=\sqrt{9\times 0}=0$ $g(\frac{1}{9})=\sqrt{9\times \frac{1}{9}}=\sqrt1=1$ $g(\frac{1}{3})=\sqrt{9\times \frac{1}{3}}=\sqrt3$ $g(1)=\sqrt{9\times 1}=3$ $g(2)=\sqrt{9\times 2}=\sqrt{18}$
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