Question

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)?

Answer 1

Answer:

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

Step-by-step explanation:

Given:

$f(x)=x^{2},g(x)=(3x)^{2}$

Here, the graph of $g(x)$ is a transformation of the parent function $f(x)$.

In order to transform $f(x)=x^{2}$ to $g(x)=(3x)^{2}$, we need to perform the following transformation:

$f(x)\rightarrow f(3x)\\x^2\rightarrow (3x)^2$

As per the transformation rules, if a positive number greater than 1 is multiplied to $x$ of the function, then the graph of the function compresses in the horizontal direction.

As 3 is multiplied to $x$ of $f(x)$, therefore, the graph of $g(x)$ is a horizontal compression by a factor of 3.