the graph above is a transformation of the function $f(x)=|x|$. write an equation for the function graphed…

Explanation:

Step1: Identify horizontal shift

The vertex of $y = |x|$ is at $(0,0)$. The vertex of the given graph is at $(- 2,-1)$. The horizontal - shift formula is $y = f(x + h)$ for a shift of $h$ units to the left. Here, $h = 2$, so we have $|x+2|$.

Step2: Identify vertical shift

The vertical - shift formula is $y=f(x)+k$ for a shift of $k$ units up or down. Since the graph is shifted 1 unit down, $k=-1$.

Answer:

$g(x)=|x + 2|-1$