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

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

Step2: Find the value of (a)

We can use a point on the graph to find (a). Let's take the point ((4,1)) (since when (x = 4), (y = 1)). Substitute (x = 4), (y = 1), (h = 0), and (k = 0) into the equation (y=a|x - h|+k). We get (1=a|4 - 0|+0), which simplifies to (1 = 4a). Solving for (a), we have (a=\frac{1}{4}).

Answer:

(g(x)=\frac{1}{4}|x|)