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

Published by Pearson

# Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 32

#### Answer

$\mathrm{See\:the\:attachment\:below.}$ #### Work Step by Step

$a).$ Find the equation of line that goes through the points $\ (0,0)\ \ \mathrm{and}\ \ (\frac{T}{2},0)\$ and the line that goes through $\ (\frac{T}{2},0)\ \ \mathrm{and}\ \ (0,1).$ Secondly, write down the domain restrictions. $\mathrm{First\:part:}$ Equation of the horizontal line is $\ y=0\$ on $\ [0,\frac{T}{2}].$ $\mathrm{Second\:part:}$ $y-0=\frac{1-0}{T-\frac{T}{2}}(x-\frac{T}{2})$ $y=\frac{2}{T}x-1\ \$ on $\ \ (\frac{T}{2},T]$ $b).$ Equation of the horizontal lines are $\ y=-A\$ and $\ y=A\$. Find the domain restrictions. $y=-A\ \$ on $\ \ [\frac{T}{2},T)\ \ and\ \ [\frac{3}{2}T,2T].$ $y=A\ \$ on $\ \ [0,\frac{T}{2})\ \ and\ \ [T,\frac{3}{2}T).$

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