Question

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

Answer 1

The second graph is the right answer.

Explanation:

The parent function is

`P(x)=|x|`

(Remember, a parent function refers to the simplest function of its type)

The image function is

`I(x)=12P(x)`

Which is
`I(x)=12|x|`.

Observe in the image attached, the image function is vertically stretched by a factor of 12.

Therefore, the right answer is the second graph.

Answer 2

The picture where the red image is the skinniest

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.