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

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

Answer

Explanation:

Step1: Identify vertex of $g(x)$

The vertex of $f(x)=|x|$ is $(0,0)$. The vertex of $g(x)$ is $(2, - 6)$.

Step2: Determine the transformation

The general form of a transformation of $y = |x|$ is $y=a|x - h|+k$, where $(h,k)$ is the vertex of the new - function. Here $h = 2$ and $k=-6$. Also, since the slope of the right - hand side of $g(x)$ is the same as that of $f(x)$ (both have a slope of 1 for $x\geq0$), $a = 1$.

Answer:

$g(x)=|x - 2|-6$