Question

Below is the graph of f(x)=In(x). how would you describe the graph of g(x)=1/3In(x)

Answer 1

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,

$k=\frac{1}{3}=0.3$

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.

Answer 2

This is the graph of f(x)=ln(x)