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

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

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

Answer

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a function (y = f(x)) across the (y) - axis is (y=f(-x)).

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

Given (f(x)=\vert x\vert), to find the reflection across the (y) - axis, we substitute (-x) for (x) in (f(x)). So (g(x)=f(-x)=\vert - x\vert). Since (\vert - x\vert=\vert x\vert) for all real numbers (x), and we need to write it in the form (a\vert x - h\vert + k). Here, (a = 1), (h = 0), and (k = 0) because (\vert x\vert=1\times\vert x - 0\vert+0).

Answer:

(1\vert x - 0\vert+0) (or simply (\vert x\vert) as (1\vert x - 0\vert+0) simplifies to (\vert x\vert))