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: 57


See the picture below.

Work Step by Step

By calculating the values of $f(x)=\mid x\mid-1$ (with blue) and $g(x)=\mid x\mid$ (with red) we can see that for every corresponding x-value, each $f(x)$ value is 1 less than the $g(x)$ value. For drawing the exact graph of the parent function here is a table of values: $g(-2)=\mid -2\mid=2$ $g(-1)=\mid -1\mid=1$ $g(0)= \mid 0\mid=0$ $g(1)= \mid 1\mid=1$ $g(2)= \mid 2\mid=2$ Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=\mid x\mid$ but translated 1 unit down. Meaning, that the transformation involves a vertical shift downwards by $1$. For drawing the exact graph of $f(x)$ here is the table of values of the given function: $f(-3)=\vert -3 \vert -1=2$ $f(-2)=\vert -2 \vert -1=1$ $f(-1)=\vert -1 \vert -1=0$ $f(0)=\vert 0 \vert -1=1$ $f(1)=\vert 1 \vert -1=2$
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