Answer :
We have the parent function:
[tex]f(x)=\log (x)[/tex]First, we are going to do a horizontal compression using the following rule:
[tex]\begin{gathered} y=f(bx) \\ so\colon \\ f(x)=\log (2x) \end{gathered}[/tex]Now, let's reflecte over y-axis:
[tex]\begin{gathered} y=f(-x) \\ so\colon \\ y=\log (-2x) \end{gathered}[/tex]Let's make a horizontal translation 4 units to the right:
[tex]\begin{gathered} y=f(x-k) \\ f(x)=\log (-2x-4) \end{gathered}[/tex]Finally, translate the function 1 unit down:
[tex]\begin{gathered} y=f(x)-h \\ f(x)=g(x)=\log (-2x-4)-1 \end{gathered}[/tex]The red graph is f(x) anf the blue graph is g(x)
