Answer :
Answer:
C. The graph g(x) is horizontally compressed by a factor of 3.
Step-by-step explanation:
Given:
[tex]f(x)=x^{2},g(x)=(3x)^{2}[/tex]
Here, the graph of [tex]g(x)[/tex] is a transformation of the parent function [tex]f(x)[/tex].
In order to transform [tex]f(x)=x^{2}[/tex] to [tex]g(x)=(3x)^{2}[/tex], we need to perform the following transformation:
[tex]f(x)\rightarrow f(3x)\\x^2\rightarrow (3x)^2[/tex]
As per the transformation rules, if a positive number greater than 1 is multiplied to [tex]x[/tex] of the function, then the graph of the function compresses in the horizontal direction.
As 3 is multiplied to [tex]x[/tex] of [tex]f(x)[/tex], therefore, the graph of [tex]g(x)[/tex] is a horizontal compression by a factor of 3.