Answer:
The g(x) represent the vertical compression by a factor of [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given : The graph of [tex]f(x)=\ln (x)[/tex]
To find : How would you describe the graph of [tex]g(x)=\frac{1}{3} \ln (x)[/tex]
Solution :
The functions are :
[tex]f(x)=\ln (x)[/tex]
[tex]g(x)=\frac{1}{3} \ln (x)[/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 [tex]\frac{1}{3}[/tex]
We plot the graph of both the functions.
Refer the attached graph below.
