Respuesta :
The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of [tex]\rm f(x) = (x-1)^2[/tex] then the function [tex]\rm g(x) = 2(x+4)^2[/tex].
Given :
- [tex]f(x) = x^2-2x+1[/tex]
- The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of [tex]f(x) = x^2-2x+1[/tex].
The following steps can be used to determine the rule for g:
Step 1 - Rewrite the given function f(x).
[tex]\rm f(x) = (x-1)^2[/tex]
Step 2 - Now, the graph is stretched vertically by a factor of 2.
[tex]= 2(x-1)^2[/tex]
Step 3 - Now, reflect the graph about the y-axis.
[tex]=2(-x-1)^2[/tex]
[tex]=2(x+1)^2[/tex]
Step 4 - Now, move to the left by 3 units.
[tex]=2(x+3+1)^2[/tex]
[tex]=2(x+4)^2[/tex]
Therefore, the function [tex]\rm g(x) = 2(x+4)^2[/tex].
For more information, refer to the link given below:
https://brainly.com/question/20381610
