Question

find g(x), where g(x) is the translation 3 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 \( y = f(x - h) \). Here, \( f(x)=\vert x\vert \), and we translate 3 units right.

Step2: Apply the rule

Substitute \( x - 3 \) into \( f(x) \). So \( g(x)=f(x - 3)=\vert x - 3\vert \). In the form \( a\vert x - h\vert + k \), \( a = 1 \), \( h = 3 \), \( k = 0 \).

Answer:

\( \vert x - 3\vert \) (or in the required form \( 1\vert x - 3\vert + 0 \))