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) = submit

Explanation:

Step1: Recall translation rules

For a function \( y = f(x) \), a horizontal translation \( h \) units left is given by \( y = f(x + h) \). Here, \( f(x)=\vert x\vert \) and we translate 6 units left.

Step2: Apply the translation

Substitute \( x \) with \( x + 6 \) in \( f(x) \). So \( g(x)=f(x + 6)=\vert x+6\vert \). Now, write it in the form \( a\vert x - h\vert + k \). We can rewrite \( \vert x + 6\vert \) as \( 1\vert x-(- 6)\vert+0 \). So \( a = 1 \), \( h=-6 \), \( k = 0 \).

Answer:

\( g(x)=1\vert x - (-6)\vert+0=\vert x + 6\vert \) (or in the required form \( 1\vert x - (-6)\vert+0 \), but usually simplified as \( \vert x + 6\vert \))