Question

find g(x), where g(x) is the translation 1 unit 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 \( y = f(x) \), a vertical translation down by \( k \) units is \( y = f(x)-k \). Here, \( f(x)=|x| \), translation 1 unit down.

Step2: Apply the rule

Original function \( f(x)=|x| \), translating 1 unit down means \( g(x)=|x| - 1 \). In the form \( a|x - h|+k \), \( a = 1 \), \( h = 0 \), \( k=-1 \), so \( g(x)=1|x - 0|+(-1)=|x|-1 \).

Answer:

\( |x| - 1 \)