which graph represents the function r(x) = |x - 2| - 1
which graph represents the function r(x) = |x - 2| - 1
Answer
Explanation:
Step1: Recall vertex - form of absolute - value function
The general form of an absolute - value function is $y=a|x - h|+k$, and its vertex is at the point $(h,k)$. For the function $r(x)=|x - 2|-1$, we have $h = 2$ and $k=-1$. So the vertex of the function $r(x)$ is at the point $(2,-1)$.
Step2: Analyze the slope
For $x\geq2$, $r(x)=(x - 2)-1=x - 3$, and the slope is $m = 1$. For $x<2$, $r(x)=-(x - 2)-1=-x + 2-1=-x+1$, and the slope is $m=-1$.
Answer:
The graph with vertex at the point $(2,-1)$ where the graph has a slope of $-1$ for $x < 2$ and a slope of $1$ for $x\geq2$. (Since no options are labeled, you need to identify the graph with vertex $(2,-1)$ among the given ones).