## University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson

# 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 $\ x.$ $\mathrm{See\:the\:graphs\:below.}$ #### 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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