The function [tex]f(x)=\sqrt{x}[/tex] is translated according to the rule
[tex](x,y)\rightarrow (x-6,y+9).[/tex]
This translation is translation 6 units to the left and 9 units up.
1. Translation of the function [tex]f(x)=\sqrt{x}[/tex] 6 units to the left gives you the function [tex]g(x)=\sqrt{x+6}.[/tex]
2. Translation of the function [tex]g(x)=\sqrt{x+6}[/tex] 9 units up gives you the function [tex]A(x)=\sqrt{x+6}+9.[/tex]
The domain of the function [tex]A(x)[/tex] is [tex][-6,\infty),[/tex] then the range of the function [tex]A(x)[/tex] is [tex][9,\infty).[/tex]
Answer: [tex][9,\infty).[/tex]
