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. g(x) =

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. g(x) =

Answer

Explanation:

Step1: Identify the vertex

The vertex of the absolute - value function (y = a|x - h|+k) is ((h,k)). The vertex of (g(x)) is at the origin ((0,0)), so (h = 0) and (k = 0).

Step2: Find the slope (a)

For (x\gt0), we can use the slope formula. Let's take two points on the right - hand side of the graph, say ((2,- 4)) and ((0,0)). The slope (a=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-4-0}{2 - 0}=-2).

Answer:

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