Question

find g(x), where g(x) is the translation 5 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 \( y = f(x) \), a vertical translation down by \( k \) units is given by \( y = f(x)-k \). Here, \( f(x)=|x| \) and we translate 5 units down.

Step2: Apply the rule

The general form is \( a|x - h|+k \). For \( f(x)=|x| \), \( a = 1 \), \( h = 0 \) (since there's no horizontal shift). A vertical shift down 5 units means \( k=- 5 \) (because shifting down subtracts from the function value). So \( g(x)=1|x - 0|+(-5)=|x|-5 \).

Answer:

\( |x| - 5 \)