Respuesta :
Given
The function is
[tex]f(x)=3\sqrt{x}[/tex]
The function g(x) transform by shifting f(x) right 3 units.
To find:
The function g(x).
Step-by-step explanation:
The translation is defined as
[tex]g(x)=f(x+a)+b[/tex]
where, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The function f(x) shifts only 3 units right. So,
[tex]a=-3,b=0[/tex]
Now,
[tex]g(x)=f(x+(-3))+0[/tex]
[tex]g(x)=f(x-3)[/tex]
[tex]g(x)=3\sqrt{x-3}[/tex] [tex][\because f(x)=3\sqrt{x}][/tex]
Therefore, the required function is [tex]g(x)=3\sqrt{x-3}[/tex].
