Answer:
The correct option is D.
Step-by-step explanation:
The given function is
[tex]G(x)=(x)^4[/tex]
It is given that the shape of F(x) and G(x) are same.
The transformation is defined as
[tex]F(x)=G(x+a)+b[/tex]
[tex]F(x)=(x+a)^4+b[/tex] ....(1)
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.
It is given that G(x) shifted four units left. It means a=4 and b=0.
Substitute a=4 and b=0 in equation (1).
[tex]F(x)=(x+4)^4+0[/tex]
[tex]F(x)=(x+4)^4[/tex]
The required function is [tex]F(x)=(x+4)^4[/tex].
Therefore the correct option is D.
