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

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

Answer

Answer:

(g(x) = 2|x|)

Explanation:

Step1: Recall the transformation formula

The general form of a transformation of (y = |x|) is (y=a|x - h|+k), where (a) is the vertical stretch or compression factor, ((h,k)) is the vertex.

Step2: Determine the vertex

The vertex of (f(x)=|x|) is ((0,0)). For (g(x)), the vertex is also ((0,0)), so (h = 0) and (k=0).

Step3: Find the value of (a)

Take a point on (g(x)), say ((1,2)). Substitute (x = 1), (y=2), (h = 0), (k = 0) into (y=a|x - h|+k). We get (2=a|1-0|+0), so (a = 2).