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

Explanation:

Step1: Identify the parent - function form

The parent function is (f(x)=|x|). The general form of a transformation of the absolute - value function is (g(x)=a|x - h|+k), where ((h,k)) is the vertex of the absolute - value function and (a) affects the slope.

Step2: Determine the vertex

The vertex of the function (g(x)) is at the origin ((0,0)), so (h = 0) and (k = 0).

Step3: Determine the slope

For (x\geq0), when (x = 2), (y = 2). The slope of the right - hand side of the absolute - value function (y = a|x|) for (x\geq0) is (a). Using the point ((2,2)) in (y = ax) (since (h = 0,k = 0) for (x\geq0)), we substitute (x = 2) and (y = 2) into (y=ax) and get (2=a\times2), so (a = 1).

Answer:

(g(x)=|x|)