Question

find g(x), where g(x) is the translation 6 units up 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 up gives \( y = f(x)+k \). Here, \( f(x)=|x| \) and we translate 6 units up.

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), and after shifting 6 units up, \( k = 6 \). So \( g(x)=1|x - 0|+6=|x| + 6 \).

Answer:

\( |x| + 6 \) (or in the form \( 1|x - 0| + 6 \))