Question

Below is the graph of f(x) = In(x). How would you describe the graph of902)gin(x)?WY321+23A. g(x) compresses f(x) by a factor ofO B. g(x) shifts f(x) vertically ſ units.C. g(x) stretches f(x) vertically by a factor of

Answer 1

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 :

`\begin{gathered} f(x)=\ln x \\ g(x)=(1)/(3)\ln (x) \end{gathered}`

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=(1)/(3)=0.3<1`

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