Answer :
Answer:
D. [tex]G(x)=x-6[/tex]
Step-by-step explanation:
Given:
Parent function:
[tex]F(x)=x[/tex]
The function is translated 6 units downwards to form new function [tex]G(x)[/tex].
Translation rules for vertical shift.
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.
For the given translation 6 units downwards would mean [tex]c=-6[/tex]
Thus the transformation statement can be given as:
[tex]F(x)\rightarrow F(x)-6[/tex] [6 units downwards]
∴ [tex]G(x)=F(x)-6[/tex]
Substituting value of [tex]F(x)[/tex].
∴ [tex]G(x)=x-6[/tex] (Answer)