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

the graph shows g(x), which is a transformation 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.

the graph shows g(x), which is a transformation 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.

Answer

Explanation:

Step1: Identify the vertex

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

Step2: Determine the slope

For $x\geq0$, the line passes through $(0,2)$ and $(2,0)$. The slope $a$ of the right - hand side of the absolute - value function is $\frac{0 - 2}{2-0}=-1$.

Answer:

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