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: 29

Answer

a) $y=x\ \ $ on $\ \ [0,1]$ $y=-x+2\ \ $ on $\ \ (1,2]$ b) $y=2\ \ $ on $\ [0,1)$ and $\ [2,3)$ $y=0\ \ $ on $\ [1,2)$ and $\ [3,4]$

Work Step by Step

$a)$ Find the equation of line that goes through the points $\ (0,0)\ \ \mathrm{and}\ \ (1,1)\ $ and the line that goes through $\ (1,1)\ \ \mathrm{and}\ \ (2,0).$ Secondly, write down the domain restrictions. $y-0=\frac{1-0}{1-0}(x-0)$ $y=x\ \ $ on $\ \ [0,1]$ $y-1=\frac{0-1}{2-1}(x-1)$ $y=-x+2\ \ $ on $\ \ (1,2]$ $b)$ We can see that the upper parts in the graph are represented with the function $\ y=2\ $ and lower parts with the function $\ y=0.$ We just need to apply restrictions on their domains. $y=2\ \ $ on $\ [0,1)$ and $\ [2,3)$ $y=0\ \ $ on $\ [1,2)$ and $\ [3,4]$
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