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 fractions. g(x) =

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 fractions. g(x) =

Answer

Explanation:

Step1: Identify the value of a

The slope of the lines on either side of the vertex of the absolute - value function remains the same as that of (y = |x|), so (a = 1).

Step2: Identify the x - coordinate of the vertex

The vertex of the function (y = |x|) is at ((0,0)). The vertex of (g(x)) is at ((0, - 6)), so (h = 0).

Step3: Identify the y - coordinate of the vertex

The y - coordinate of the vertex of (g(x)) is (k=-6).

Answer:

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