Answer
See Graph I
![](https://gradesaver.s3.amazonaws.com/uploads/solution/349132ee-d19d-4039-8629-8bfac58a29f5/result_image/1506492590.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015447Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=55d26f929a34f482e1da6822ce28dea67dd751b3605e1df1673e40c3fa670654)
Work Step by Step
For $y = x^2 + 3,$
when
$x = 2, y = 7;$
$x = 1, y = 4;$
$x = 0, y = 3;$
$x = −1, y = 4;$
$x = −2, y = 7$
As seen, $y = x^2 + 3$ is the vertical translation of $y = x^2$ up by 3 units also.
Domain = $(−\infty, \infty)$
Range = $[3, \infty)$