Answer
Refer to the curve in Black in Graph I
Work Step by Step
For $y = |x + 3| + 2,$
when
$x = 1, y = 6;$
$x = -1, y = 4;$
$x = -3, y = 2;$
$x = -5, y = 4;$
$x = -7, y = 6$
As seen, $y = |x + 3| + 2$ is the horizontal translation to the left by 3 units and vertical translation up by 2 units of $y = |x|$ as well.
Domain = $(−\infty, \infty)$
Range = $[2, \infty)$