Question

find g(x), where g(x) is the translation 3 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 \( y = f(x + h) \). Here, \( f(x)=\vert x\vert \), and we translate 3 units left.

Step2: Apply the translation

Substitute \( x+3 \) into \( f(x) \). So \( g(x)=f(x + 3)=\vert x+3\vert \). Now, write it in the form \( a\vert x - h\vert + k \). We can rewrite \( \vert x + 3\vert \) as \( \vert x-(- 3)\vert+0 \), so \( a = 1 \), \( h=-3 \), \( k = 0 \).

Answer:

\( 1\vert x - (-3)\vert + 0 \) (or simplified as \( \vert x + 3\vert \))