Question

find g(x), where g(x) is the translation 3 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 gives \( y = f(x)-k \). Here, \( f(x)=|x| \) and we translate 3 units down.

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

The general form is \( a|x - h|+k \). For \( f(x)=|x| \), \( a = 1 \), \( h = 0 \) (since there's no horizontal shift). Translating 3 units down means \( k=- 3 \) (because down is negative in vertical translation). So \( g(x)=1|x - 0|+(-3)=|x|-3 \).

Answer:

\( |x| - 3 \)