Question

find g(x), where g(x) is the translation 6 units right 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 \( h \) units right gives \( y = f(x - h) \), and \( k \) units up gives \( y = f(x)+k \). The vertical stretch/compression is \( a \).
Here, \( f(x)=|x| \), translation 6 units right, no vertical stretch/compression (\( a = 1 \)) and no vertical shift (\( k = 0 \)).

Step2: Apply the rule

Substitute \( x \) with \( x - 6 \) in \( f(x) \). So \( g(x)=|x - 6|+0 \), which is \( g(x)=1|x - 6|+0 \) (since \( a = 1 \), \( h = 6 \), \( k = 0 \)).

Answer:

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