Question

find g(x), where g(x) is the translation 2 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 transformation rules

For a function \( y = f(x) \), a vertical translation down by \( k \) units is given by \( y = f(x)-k \). Here, \( f(x)=|x| \) and we translate down by 2 units.

Step2: Apply the transformation

Using the rule, \( g(x)=f(x)-2 \). Substituting \( f(x)=|x| \), we get \( g(x)=|x| - 2 \). In the form \( a|x - h|+k \), \( a = 1 \), \( h = 0 \), \( k=-2 \), so \( g(x)=1|x - 0|+(-2)=|x|-2 \).

Answer:

\( |x| - 2 \)