find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=x ). write your answer in…

find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=x ). write your answer in the form ( mx + b ), where ( m ) and ( b ) are integers. ( g(x)= )

find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=x ). write your answer in the form ( mx + b ), where ( m ) and ( b ) are integers. ( g(x)= )

Answer

Explanation:

Step1: Recall the reflection rule

When a function (y = f(x)) is reflected across the (x -)axis, the transformation rule is (y=-f(x)).

Step2: Apply the rule to (f(x)=x)

Given (f(x) = x), then (g(x)=-f(x)). Substitute (f(x)) into the formula: (g(x)=-x), which can be written in the form (mx + b) as (g(x)=-1x+0).

Answer:

(g(x)=-x) (or (g(x)=- 1x + 0))