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If you shift the linear parent function, F(x) = x, down 6 units,
what is the equation of the new function?
O A. G(X) = 6x
O B. G(x) = x
OC. G(x) = x+6
D. G(x) = x-6

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)

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