Question

find g(x), where g(x) is the translation 6 units left 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 \( y = f(x) \), a horizontal translation \( h \) units left is given by \( y = f(x + h) \). There's no vertical stretch (\( a = 1 \)) or vertical shift (\( k = 0 \)) here.

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

We need to translate \( f(x)=\vert x\vert \) 6 units left. Using the rule, substitute \( x \) with \( x + 6 \). So \( g(x)=\vert x - (-6)\vert+ 0 \) (in the form \( a\vert x - h\vert + k \), here \( a = 1 \), \( h=-6 \), \( k = 0 \)). Thus, \( g(x)=\vert x + 6\vert \) or \( 1\vert x - (-6)\vert+ 0 \).

Answer:

\( 1\vert x - (-6)\vert + 0 \) (or simplified as \( \vert x + 6\vert \))