Question

If the graph of function g is 6 units below the graph of function f, which could be function g? f(x) = -2x + 7 A. g(x) = -2x + 1 B. g(x) = -2x − 6 C. g(x) = -6x + 7 D. g(x) = -2x + 20

Answer 1

A.
`g(x)=-2x+1`

Explanation:

Given:

`f(x)=-2x+7`

The function
`f(x)` is shifted 6 units below which forms the function
`g(x)`

To find the function
`g(x)`, we apply the following translation rules:

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

If
`c>0` the function
`f(x)` shifts
`c` units up.

If
`c<0` the function
`f(x)` shifts
`c` units down.

Since the function
`f(x)` is shifting 6 units below, thus value of
`c<0` which is taken as -6.

The translation occurring here is given by:

`f(x)\rightarrow f(x)-6`

Thus,

`g(x)=f(x)-6`

Substituting
`f(x)=-2x+7`

`g(x)=-2x+7-6`

∴
`g(x)=-2x+1`