select the correct answer.\nif $g(x)=f(\\frac{1}{3}x)$, which statement is true?\na. the graph of function…

select the correct answer.\nif $g(x)=f(\\frac{1}{3}x)$, which statement is true?\na. the graph of function $f$ is stretched vertically by a scale factor of 3 to create the graph of function $g$.\nb. the graph of function $f$ is stretched horizontally by a scale factor of 3 to create the graph of function $g$.\nc. the graph of function $f$ is compressed horizontally by a scale factor of $\\frac{1}{3}$ to create the graph of function $g$.\nd. the graph of function $f$ is compressed vertically by a scale factor of $\\frac{1}{3}$ to create the graph of function $g$.

select the correct answer.\nif $g(x)=f(\\frac{1}{3}x)$, which statement is true?\na. the graph of function $f$ is stretched vertically by a scale factor of 3 to create the graph of function $g$.\nb. the graph of function $f$ is stretched horizontally by a scale factor of 3 to create the graph of function $g$.\nc. the graph of function $f$ is compressed horizontally by a scale factor of $\\frac{1}{3}$ to create the graph of function $g$.\nd. the graph of function $f$ is compressed vertically by a scale factor of $\\frac{1}{3}$ to create the graph of function $g$.

Answer

Explanation:

Step1: Recall transformation rule

For a function $y = f(kx)$ where $k>0$, if $0 < k< 1$, the graph of $y = f(x)$ is stretched horizontally. Here $k=\frac{1}{3}$.

Step2: Analyze the transformation

When $g(x)=f(\frac{1}{3}x)$, compared to the graph of $y = f(x)$, the graph of $y = g(x)$ is stretched horizontally. The scale - factor of the horizontal stretch is $\frac{1}{k}=3$.

Answer:

B. The graph of function $f$ is stretched horizontally by a scale factor of 3 to create the graph of function $g$.