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Answer:
[tex]g(x)=3(x-3)+3[/tex]
Step-by-step explanation:
Translations
[tex]\textsf{For}\quad a > 0[/tex]
[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]
Parent function: [tex]f(x)=3x[/tex]
Translated 4 units right: [tex]f(x-4)=3(x-4)[/tex]
Translated 3 units up: [tex]f(x-4)+3=3(x-4)+3[/tex]