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Suppose f(x)=x^2 and g(x)=(3x)^2 which statement best compares the graph of g(x) with the graph of f(x)?

A.the graph of g(x) is vertically stretched by a factor of 3

B. The graph of g(x) is shifted to the right

C.the graph of g(x) is horizontally compressed by a factor of 3

D.the graph g(x) is horizontally stretched by a factor of 3

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.

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