First, lets perform each transformation and then take a look at its graph:
1.
[tex]\begin{gathered} g(x)=-\frac{1}{2}f(x-2) \\ \\ \Rightarrow g(x)=-\frac{1}{2}\ln (x-2) \end{gathered}[/tex]
The only etiquette that matches this plot is: Function decreases as x increases
2.
[tex]\begin{gathered} h(x)=f(x-\frac{1}{2}) \\ \\ \Rightarrow h(x)=\ln (x-\frac{1}{2}) \end{gathered}[/tex]
The only etiquette that matches this plot is: x-intercept at (1.5 , 0)
3.
[tex]\begin{gathered} j(x)=f(x)-\frac{1}{2} \\ \\ \Rightarrow j(x)=\ln (x)-\frac{1}{2} \end{gathered}[/tex]
The only etiquette that matches this plot is: Asymptote of x = 0
