Answer:
Option B - [tex]g(x)=3x^2[/tex]
Step-by-step explanation:
Given : The function f(x) and g(x) are shown in the graph.
To find : What is g(x)?
Solution :
The parent function [tex]f(x)=x^2[/tex]
with the vertex (0,0)
The graph of g(x) is the translation of f(x)
The parent function is horizontally compressed.
Transformation to horizontally compressed,
f(x)→f(bx) , the graph of f(x) is horizontally compressed by b unit.
And the graph of [tex]g(x)=3x^2[/tex]
with the vertex (0,0)
As [tex]g(x)=3x^2[/tex] also satisfied the point (2,12).
[tex]g(x)=3(2)^2=3(4)=12[/tex]
Refer the attached graph below.
Therefore, Option B is correct.
