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: 19

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 $g(x)=\vert -\frac{1}{2} x\vert$ (with blue) will be wider, as the coefficient multiplies each y-value of the parent function by $-\frac{1}{2}$ However, it will not be reflected across the y-axis, as the minus sign is inside the absolute value sign. 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 will be shrinked by a factor of $2$. For drawing the exact graph of $g(x)$ here is the table of values of the given function: $g(-2)=\mid -\frac{1}{2}\times -2\mid=1$ $g(-1)=\mid -\frac{1}{2}\times -1\mid=\frac{1}{2}$ $g(0)=\mid -\frac{1}{2}\times 0\mid=0$ $g(1)=\mid -\frac{1}{2}\times1\mid=\frac{1}{2}$ $g(2)=\mid -\frac{1}{2}\times 2\mid=1$
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