Answer
Refer to the curve in Black in Graph I
![](https://gradesaver.s3.amazonaws.com/uploads/solution/a271989a-a464-4585-a4d4-a7331fd1252b/result_image/1506958362.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013938Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=cbbfb272512159d7c803f3491f8305c502cc397030f9f069b92c514293ea4011)
Work Step by Step
For $f(x) = -3(x - 2)^2 + 1,$
when
$x = 4, y = -11;$
$x = 3, y = -2;$
$x = 2, y = 1;$
$x = 1, y = -2;$
$x = 0, y = -11$
As seen, $f(x) = -3(x - 2)^2 + 1$ is the horizontal translation to the right by 2 units, the vertical stretching by three times, the reflection across the $x$-axis and the vertical translation up by 1 unit of $f(x) = x^2$.
Domain = $(−\infty, \infty)$
Range = $(-\infty, 1]$