University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 24

Answer

$\mathrm{Remember:}\ $ We can consider vertical line test to see if the graph is a function of $\ x\ $ or not. If a vertical line, let's say $\ \ x=a\ \ $ intersects the graph at any two points, the graph would not be a function of $\ x.\ $ In both these cases, there exist a real number $\ a\ $ for which the vertical line $\ x=a\ $ intersects the graphs of $\ |x|+|y|=1\ $ and $\ |x+y|=1\ $ in two points. So, they both are not functions of $\ x.$ $\mathrm{See\:the\:graphs\:below.}$
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Work Step by Step

$a).$ When $\ x=0,\ |y|=1\ \rightarrow\ \ y=\pm1.\ $ When $\ y=0,\ |x|=1\ \rightarrow\ \ x=\pm1.\ $ So, we will have 4 different points for the given function. As we can see the given function is linear, just connect these 4 points with line segments. $b).$ For the absolute value equation, we always get two solutions. These are $\ \ x+y=1\ \ \mathrm{and}\ \ -x-y=1.$ Just graph these lines.
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