which equation represents the function graphed on the coordinate plane?\n$g(x)=|x + 1|+3$\n$g(x)=|x +…
which equation represents the function graphed on the coordinate plane?\n$g(x)=|x + 1|+3$\n$g(x)=|x + 3|-1$\n$g(x)=|x - 1|+3$\n$g(x)=|x + 3|+1$
Answer
Explanation:
Step1: Recall vertex - form of absolute - value function
The general form of an absolute - value function is $y=a|x - h|+k$, where $(h,k)$ is the vertex of the absolute - value function graph.
Step2: Identify the vertex of the given graph
From the graph, the vertex of the absolute - value function is at the point $(-1,3)$.
Step3: Substitute the vertex values into the general form
Substituting $h=-1$ and $k = 3$ into $y=a|x - h|+k$ (with $a = 1$ since the slope of the rays is 1), we get $y=|x-(-1)|+3=|x + 1|+3$.
Answer:
$g(x)=|x + 1|+3$