Question

find g(x), where g(x) is the translation 8 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) = submit

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 \( y = f(x)+k \). Here, no vertical translation, so \( k = 0 \), and horizontal translation 8 units right, so \( h = 8 \). The original function \( f(x)=\vert x\vert \), so \( a = 1 \) (no vertical stretch/compression or reflection).

Step2: Apply the translation

Substitute into the form \( a\vert x - h\vert + k \). We have \( a = 1 \), \( h = 8 \), \( k = 0 \). So \( g(x)=1\vert x - 8\vert+0=\vert x - 8\vert \).

Answer:

\( \vert x - 8\vert \)