Answer
$a.\quad \mathbb{R}$
$b.\quad (-3,0),\ (-1.5,0)$, ($0,-3$)
$c.\quad $see image
$d.\quad (-\infty,1]$
$e.\quad $Continuous
Work Step by Step
It's best to graph the function first.
Left of x=-2, (excluding x=-2)
the graph is the line $y=x+3$, containing points $(-5,-2)$ and $(-3,0)$
Right of x=-2 (including x=-2)
the graph is the line $y=-2x-3$, containing points ($-2,1$) and ($0,-3$)
Domain: whole set $\mathbb{R}$
Range : $(-\infty,1]$
x-intercepts:$\quad (-3,0)$ and $(-1.5,0)$.
y intercepts:$\quad$ ($0,-3$)
There are no breaks, holes or gaps in the graph - it is continuous.