Question

the graph above is a transformation of the function f(x)=|x|. write an formula for the function graphed above: g(x)= question help: □ video

Explanation:

Step1: Identify the vertex

The vertex of $y = |x|$ is at $(0,0)$. The vertex of the given graph is at $(0, - 2)$. So, there is a vertical - shift of 2 units down.

Step2: Identify the slope

For $y = |x|$, the slope of the right - hand side of the vertex is 1 and the left - hand side is - 1. For the given graph, the slope of the right - hand side of the vertex is - 1 and the left - hand side is 1. This indicates a reflection about the $y$ - axis and a change in slope. The general form of a transformation of $y = |x|$ is $y=a|x - h|+k$, where $(h,k)$ is the vertex. Here, $h = 0,k=-2$ and $a=-1$.

Step3: Write the formula

The formula for the function $g(x)$ is $g(x)=-|x|-2$.

Answer:

$g(x)=-|x|-2$