Question

find g(x), where g(x) is the translation 10 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 10 units up.

Step2: Determine \( a \), \( h \), \( k \)

The general form is \( a\vert x - h\vert + k \). For \( f(x)=\vert x\vert \), \( a = 1 \) (no vertical stretch/compression), \( h = 0 \) (no horizontal shift), and \( k = 10 \) (10 units up). So \( g(x)=1\vert x - 0\vert+ 10=\vert x\vert + 10 \).

Answer:

\( \vert x\vert + 10 \) (or in the form \( 1\vert x - 0\vert + 10 \))