Step-by-step explanation:
Given : The graph of f(x) = In (x)
To find : How would you describe the graph of g(x) = In(x)/3
Solution :
The functions are :
[tex]\begin{gathered} f(x)=\ln x \\ g(x)=\frac{1}{3}\ln (x) \end{gathered}[/tex]
g(x) is in the form of,
[tex]g(x)=kf(x)[/tex]
Where, k is stretch factor.
If k>1, then it represents vertical stretch
If k<1, then it represents vertical compression.
We know,
[tex]k=\frac{1}{3}=0.3<1[/tex]
The g(x) represent the vertical compression by a factor of
We plot the graph of both the functions.
The g(x) represent the vertical compression by a factor of
Refer the attached graph below.
Therefore g(x) compresses f(x) by a factor of 1/3
Hence the correct answer is Option A
