Answer
Refer to the curve in Black in Graph I
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ee218c52-c25b-47b4-a7f3-793de00a0754/result_image/1506944143.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021926Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=05b98a1214d9aac5caf8adc29d8c91217ee0f1ef2a4bfceabec089d05ec99a3a)
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 = $[2, \infty)$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ee218c52-c25b-47b4-a7f3-793de00a0754/steps_image/small_1506944143.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021926Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=e77ed434321cb7b06b4afb7835cceb9c4e07d7c506db1acfdd89dc080c26c50e)