Which of the following graphs shows the preimage P(x)=|x| and the image I(x)=12⋅P(x)?




Answer:
The picture where the red image is the skinniest
Step-by-step explanation:
The graph P(x) is the parent graph for all absolute functions. It has a vertex of (0,0) and has the following points:
x f(x)
-2 2
-1 1
0 0
1 1
2 2
The image of l(x) = 12P(x) changes the points of the function to
x f(x)
-2 24
-1 12
0 0
1 12
2 24
This makes the graph much skinnier. The graph with the skinniest red graph is the graph.
Answer:
Step-by-step explanation:
The parent function is
[tex]P(x)=|x|[/tex]
(Remember, a parent function refers to the simplest function of its type)
The image function is
[tex]I(x)=12P(x)[/tex]
Which is [tex]I(x)=12|x|[/tex].
Observe in the image attached, the image function is vertically stretched by a factor of 12.
Therefore, the right answer is the second graph.