the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x). write your…

the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x). write your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions. g(x) =

the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x). write your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions. g(x) =

Answer

Explanation:

Step1: Identify the vertex of $g(x)$

The vertex of $f(x)=|x|$ is $(0,0)$. The vertex of $g(x)$ is $(2,0)$. So $h = 2$ and $k=0$.

Step2: Determine the value of $a$

The slope of the right - hand side of $f(x)=|x|$ is 1. For $g(x)$, when $x>2$, if we take a point like $(4,2)$ on $g(x)$. Using the point - slope form with the vertex $(2,0)$ and the point $(4,2)$ for the linear part of the absolute - value function. The slope of the right - hand side of $g(x)$ is $a = 1$.

Answer:

$g(x)=1|x - 2|+0=|x - 2|$