Question

If the graph of function gis 6 units below the graph of function f, which could be function g?

Rx) = -2x +7

O A. g(x) = -6x + 7
OB. 8x) = -2x + 1
OC. X) =-2x + 20
D. g(x) = -2x - 6

Answer 1

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

Explanation:

Given:

The given function is:

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

The graph of another function 'g' is 6 units below the graph of the given function 'f'.

In other words, we can say that the graph of function 'g' is the transformation of function 'f' and the transformation is a translation by 6 units down as the graph of
`g(x)` is below the graph of
`f(x)`

Thus, as per the rules of transformation,

If a graph is shifted down by 'C' units where 'C' is a positive number, then the function rule is given as:

`f(x)\to f(x)-C`

Here,
`C=6`

Therefore, the equation of
`g(x)` is given as:

`g(x)=f(x)-6\\g(x)=-2x+7-6\\g(x)=-2x+1`

So, the option B is the correct answer.