Answer
$a.\quad [-2,\infty)$
$b.\quad (2,0)$, ($0,3$)
$c.\quad $see image
$d.\quad (-\infty,4)\cup\{5\}$
$e.\quad $Not continuous (jump at x=1)
Work Step by Step
It's best to graph the function first.
For $x\in[-2,1)$
the graph is the line segment on the line $y=x+3$,
containing points $(-2,1)$ and $(0,3)$
The right end of the line segment is marked with an open dot at (1,4).
At x=1, the point (1,5) is on the graph. (A jump on the graph - not continuous)
for $x\in(1,\infty)$
the graph is the ray $y=-x+2$, with the point (1,1) excluded (open dot)
containing points $(2,0)$ and $(4,-2)$
Domain: $[-2,\infty)$
Range : $(-\infty,4)\cup\{5\}$
x-intercepts:$\quad (2,0)$.
y intercepts:$\quad$ ($0,3$)
There is a jump on the graph at x=1 - not continuous