Answer:
Translations
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=-\:f\:(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f\:(-\:x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Parent function: [tex]f\:(x) = \ln(x)[/tex]
Translated right 1 unit: [tex]f\:(x\:-1) = \ln(x - 1)[/tex]
Then translated down 9 units: [tex]f\:(x\: -1)-9 = \ln(x - 1) - 9[/tex]
The reflected over the x-axis: [tex]-\:[f\:(x\:-1) - 9] = -\ln(x - 1) + 9[/tex]
Therefore, [tex]g(x) = -\ln\:(x\:- 1) + 9[/tex]
⇒ g(30) = - ln(30 - 1) + 9
= -3.36729... + 9
= 5.6 (nearest tenth)
