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

find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=|x| ).\nwrite your answer in the form ( a|x - h|+k ), where ( a ), ( h ), and ( k ) are integers.\n( g(x)= )

find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=|x| ).\nwrite your answer in the form ( a|x - h|+k ), where ( a ), ( h ), and ( k ) are integers.\n( g(x)= )

Answer

Explanation:

Step1: Recall the reflection rule

When a function (y = f(x)) is reflected across the (x -)axis, the transformation is (y=-f(x)). Given (f(x)=\vert x\vert), then (g(x)=-f(x)).

Step2: Substitute (f(x)) into the reflection formula

Substitute (f(x)=\vert x\vert) into (g(x)=-f(x)). We get (g(x)=-\vert x\vert). In the form (a\vert x - h\vert+k), here (a=- 1), (h = 0), and (k = 0). So (g(x)=-1\vert x-0\vert + 0).

Answer:

(-\vert x\vert) (or (-1\vert x - 0\vert+0))