Question

find g(x), where g(x) is the translation 2 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, \( f(x)=|x| \) and we translate 2 units left.

Step2: Apply the translation

Substitute \( x \) with \( x + 2 \) in \( f(x) \). So \( g(x)=f(x + 2)=|x + 2| \). In the form \( a|x - h|+k \), we can rewrite \( |x + 2| \) as \( 1|x - (-2)|+0 \), so \( a = 1 \), \( h=-2 \), \( k = 0 \).

Answer:

\( g(x)=|x + 2| \) (or in the form \( 1|x - (-2)|+0 \), but \( |x + 2| \) is simpler and meets the integer requirements for \( a = 1 \), \( h=-2 \), \( k = 0 \))