Question

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 1

D.
`G(x)=x-6`

Explanation:

Given:

Parent function:

`F(x)=x`

The function is translated 6 units downwards to form new function
`G(x)`.

Translation rules for vertical shift.

`f(x)\rightarrow f(x)+c`

If
`c>0` the function shifts
`c` units to the up.

If
`c<0` the function shifts
`c` units to the down.

For the given translation 6 units downwards would mean
`c=-6`

Thus the transformation statement can be given as:

`F(x)\rightarrow F(x)-6` [6 units downwards]

∴
`G(x)=F(x)-6`

Substituting value of
`F(x)`.

∴
`G(x)=x-6` (Answer)