Question

The graph of g(x) is the graph of f(x)=x+6 reflected across the x-axis. Which equation describes the function g?

A. g(x)=x−6
B. g(x)=−x−6
C. g(x)=−6x−6
D. g(x)=−x+6

Answer 1

I took the test and this was the answer

Answer 2

ANSWER

The correct answer is
`g(x)=-x-6`

Step-by-step explanation

The mapping for reflection across the x-axis is given by
`(x,-y)`

Given
`f(x)=x+6`. We can let
`y=x+6`

we can write the ordered pair
`(x,y)` or
`(x,x+6)` as the ordered pair of the preimage of
`f`.

The image function will have the ordered pair
`(x,-y)`

or


`(x,-x-6)`.

That is, we negate all the y-coordinates.

Therefore


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