Question

find g(x), where g(x) is the translation 9 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/down gives \( y = f(x)+k \). The vertical stretch/compression is \( a \).

Step2: Apply translation to \( f(x)=\vert x\vert \)

We need to translate \( f(x)=\vert x\vert \) 9 units right. So using the rule for horizontal translation (right by \( h = 9 \)), and since there's no vertical stretch (\( a = 1 \)) or vertical translation (\( k = 0 \)), we substitute into \( a\vert x - h\vert + k \).
So \( g(x)=1\vert x - 9\vert+0=\vert x - 9\vert \).

Answer:

\( \vert x - 9\vert \) (or in the form \( 1\vert x - 9\vert+0 \))