Question

find g(x), where g(x) is the translation 8 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, \( f(x)=\vert x\vert \), and we translate 8 units up.

Step2: Apply the rule to \( f(x) \)

The general form is \( a\vert x - h\vert + k \). For \( f(x)=\vert x\vert \), \( a = 1 \), \( h = 0 \) (since there's no horizontal shift), and after translating 8 units up, \( k = 8 \). So \( g(x)=\vert x - 0\vert+ 8=1\vert x - 0\vert + 8 \).

Answer:

\( g(x)=1\vert x - 0\vert + 8 \) (or simplified as \( g(x)=\vert x\vert + 8 \))