Question

find g(x), where g(x) is the translation 6 units down of f(x) = |x|. write your answer in the form a|x - h| + k, where a, h, and k are integers. g(x) =

Explanation:

Step1: Recall translation rules

For a function \( y = f(x) \), translating it \( k \) units down means \( y = f(x) - k \). Here, \( f(x)=\vert x\vert \), and we translate 6 units down.

Step2: Determine \( a, h, k \)

The general form is \( a\vert x - h\vert + k \). For \( f(x)=\vert x\vert \), \( a = 1 \), \( h = 0 \) (since there's no horizontal shift). Translating 6 units down means \( k=- 6 \). So \( g(x)=1\vert x - 0\vert-6 \), which simplifies to \( g(x)=\vert x\vert - 6 \).

Answer:

\( g(x)=\vert x\vert - 6 \) (or in the form \( 1\vert x - 0\vert+(-6) \))