Answer:
The g(x) represent the vertical compression by a factor of \(\frac{1}{3}\)
Step-by-step explanation:
Given : The graph of \(f(x)=\ln (x)\)
To find : How would you describe the graph of \(g(x)=\frac{1}{3} \ln (x)\)
Solution :
The functions are :
\(f(x)=\ln (x)\)
\(g(x)=\frac{1}{3} \ln (x)\)
g(x) is in the form of,
\(g(x)=kf(x)\)
Where, k is stretch factor.
If k>1, then it represents vertical stretch
If k<1, then it represents vertical compression.
We know,
\(k=\frac{1}{3}=0.3<1\)
The g(x) represent the vertical compression by a factor of \(\frac{1}{3}\)
We plot the graph of both the functions.
Refer the attached graph below.
