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: 9

Answer

See the picture below.
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Work Step by Step

The parent function is $y=|x|$ (in red), but the graph of $g(x)=\frac{2}{3}|x|$ (in blue) will be wider, as the coefficient multplies each y-value of the parent function by $\frac{2}{3}$. By the use of graph transformation techniques, the graph is shrinked by a factor of $\frac{3}{2}$. For drawing the exact graph of $g(x)$ here is the table of values of the given function: $f(-3)=\frac{2}{3}\vert -3\vert=2$ $f(-1)=\frac{2}{3}\vert -1\vert=\frac{2}{3}$ $f(0)=\frac{2}{3}\vert 0\vert=0$ $f(1)=\frac{2}{3}\vert 1\vert=\frac{2}{3}$ $f(3)=\frac{2}{3}\vert 3\vert=2$
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