Question

the graph of y = |x| is the solid black graph below. which function represents the dotted graph? answer y = |x + 1| + 3 y = |x - 1| + 3 y = |x + 1| - 3 y = |x - 1| - 3 submit answer

Explanation:

Step1: Recall transformation rules

The general form of a transformation of the absolute - value function $y = |x|$ is $y=a|x - h|+k$, where $(h,k)$ is the vertex of the transformed function. The vertex of $y = |x|$ is $(0,0)$.

Step2: Identify the vertex of the dotted graph

By observing the graph, the vertex of the dotted graph is at $(- 1,3)$.

Step3: Determine the transformation function

For the absolute - value function $y=a|x - h|+k$, when the vertex is $(h,k)=(-1,3)$, the function is $y = |x+1| + 3$ (since $h=-1$ and $k = 3$ and $a = 1$ as the shape of the absolute - value graph is not stretched or compressed).

Answer:

$y = |x + 1|+3$