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: 18

Answer

See the picture below.
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Work Step by Step

The parent function is $f(x)=\vert x\vert$ (with red), but the graph of $g(x)=-2\vert x\vert$ (with blue) will be narrower, as the coefficient multplies each y-value of the parent function by $2$ and will also be reflected across the x-axis because of the coefficient of $-1$. For drawing the exact graph of the parent function here is a table of values: $f(-2)=\mid -2\mid=2$ $f(-1)=\mid -1\mid=1$ $f(0)= \mid 0\mid=0$ $f(1)= \mid 1\mid=1$ $f(2)= \mid 2\mid=2$ By the use of graph transformation techniques, the graph is stretched by a factor of $2$ and will also be reflected across the x-axis. For drawing the exact graph of $g(x)$ here is the table of values of the given function: $g(-2)=-2 \mid -2\mid=-4$ $g(-1)=-2 \mid -1\mid=-2$ $g(0)=-2 \mid 0\mid=0$ $g(1)=-2 \mid 1\mid=-2$ $g(2)=-2 \mid 2\mid=-4$
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