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 $\ \ [0,\frac{T}{2})\ \ and\ \ [T,\frac{3}{2}T).$
