Answer:
A. [tex]g(x)=-2x+1[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=-2x+7[/tex]
The function [tex]f(x)[/tex] is shifted 6 units below which forms the function [tex]g(x)[/tex]
To find the function [tex]g(x)[/tex], we apply the following translation rules:
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units up.
If [tex]c<0[/tex] the function [tex]f(x)[/tex] shifts [tex]c[/tex] units down.
Since the function [tex]f(x)[/tex] is shifting 6 units below, thus value of [tex]c<0[/tex] which is taken as -6.
The translation occurring here is given by:
[tex]f(x)\rightarrow f(x)-6[/tex]
Thus,
[tex]g(x)=f(x)-6[/tex]
Substituting [tex]f(x)=-2x+7[/tex]
[tex]g(x)=-2x+7-6[/tex]
∴ [tex]g(x)=-2x+1[/tex]
