Question

if ( g(x) = f(4x) ), which statement is true?

a. the graph of function ( f ) is stretched horizontally by a scale factor of 4 to create the graph of function ( g ).

b. the graph of function ( f ) is compressed vertically by a scale factor of ( \frac{1}{4} ) to create the graph of function ( g ).

c. the graph of function ( f ) is compressed horizontally by a scale factor of ( \frac{1}{4} ) to create the graph of function ( g ).

d. the graph of function ( f ) is stretched vertically by a scale factor of 4 to create the graph of function ( g ).

Explanation:

Step1: Recall horizontal transformation rules

For a function $g(x) = f(kx)$, when $k>1$, the graph of $f(x)$ is horizontally compressed by a scale factor of $\frac{1}{k}$.

Step2: Match to given function

Here, $g(x)=f(4x)$, so $k=4$. The scale factor is $\frac{1}{4}$, meaning $f(x)$ is horizontally compressed by $\frac{1}{4}$ to get $g(x)$.

Answer:

C. The graph of function $f$ is compressed horizontally by a scale factor of $\frac{1}{4}$ to create the graph of function $g$