Question

Given f(x) = ln(x), which is the correct answers ?

Answer 1

First, lets perform each transformation and then take a look at its graph:

1.

`\begin{gathered} g(x)=-(1)/(2)f(x-2) \\ \\ \Rightarrow g(x)=-(1)/(2)\ln (x-2) \end{gathered}`

The only etiquette that matches this plot is: Function decreases as x increases

2.

`\begin{gathered} h(x)=f(x-(1)/(2)) \\ \\ \Rightarrow h(x)=\ln (x-(1)/(2)) \end{gathered}`

The only etiquette that matches this plot is: x-intercept at (1.5 , 0)

3.

`\begin{gathered} j(x)=f(x)-(1)/(2) \\ \\ \Rightarrow j(x)=\ln (x)-(1)/(2) \end{gathered}`

The only etiquette that matches this plot is: Asymptote of x = 0