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

the graph shows $g(x)$, which is a translation 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$g(x)=$

the graph shows $g(x)$, which is a translation 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)=|x| + 9)

Explanation:

Step1: Recall the vertex form of absolute - value function

The vertex form of an absolute - value function is (y = a|x - h|+k), where ((h,k)) is the vertex of the graph.

Step2: Identify the vertex of (g(x))

For the function (f(x)=|x|), its vertex is ((0,0)). For the function (g(x)), from the graph, the vertex is ((0,9)), so (h = 0) and (k=9).

Step3: Determine the value of (a)

The slope (the value of (a)) of the right - hand side of (f(x)=|x|) (for (x\geq0), (y = x)) and the right - hand side of (g(x)) (for (x\geq0), if (x = 1), (y=1 + 9)) is (a = 1) (since the "width" of the graph of (g(x)) is the same as that of (f(x))). Substitute (a = 1), (h = 0), and (k = 9) into the vertex form (y=a|x - h|+k). We get (g(x)=1|x-0| + 9), which simplifies to (g(x)=|x|+9).