Question

find g(x), where g(x) is the translation 9 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 \( y = f(x + h) \).

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

We need to translate \( f(x)=\vert x\vert \) 9 units left. So substitute \( x \) with \( x + 9 \) in \( f(x) \).
Thus, \( g(x)=\vert x + 9\vert \). Now, write it in the form \( a\vert x - h\vert + k \). We can rewrite \( \vert x + 9\vert \) as \( 1\vert x - (-9)\vert + 0 \), so \( a = 1 \), \( h=-9 \), \( k = 0 \).

Answer:

\( 1|x - (-9)| + 0 \) (or simply \( |x + 9| \) which is equivalent in this form as \( 1|x - (-9)| + 0 \))