the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x).
the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x).
Answer
Explanation:
Step1: Identify vertex of $f(x)$ and $g(x)$
The vertex of $f(x)=|x|$ is $(0,0)$. The vertex of $g(x)$ from the graph is $(5, - 9)$.
Step2: Use translation rule for absolute - value functions
The general form of a translation of $y = |x|$ is $y=|x - h|+k$, where $(h,k)$ is the vertex of the new function. Here $h = 5$ and $k=-9$. So $g(x)=|x - 5|-9$.
Answer:
$g(x)=|x - 5|-9$