Question

find g(x), where g(x) is the translation 10 units down 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 \( y = f(x) \), translating it \( k \) units down gives \( y = f(x) - k \). Here, \( f(x)=\vert x\vert \), and we translate 10 units down. Also, the form is \( a\vert x - h\vert + k \). For \( f(x)=\vert x\vert \), \( a = 1 \), \( h = 0 \) (since there's no horizontal shift), and after shifting down 10 units, \( k=- 10 \).

Step2: Construct \( g(x) \)

Using the form \( a\vert x - h\vert + k \), with \( a = 1 \), \( h = 0 \), and \( k=-10 \), we get \( g(x)=1\vert x - 0\vert+(- 10)=\vert x\vert - 10 \).

Answer:

\( g(x)=\vert x\vert - 10 \) (or in the form \( 1\vert x - 0\vert - 10 \))