Question

Which of the following graphs shows the preimage P(x)=x^2 and the image I(x)=P(1/3x)?

Answer 1

(See explanation and attachment below)

Explanation:

The image is equal to:

`I(x) = \left((1)/(3)\cdot x \right)^(2)`

`I(x) = (1)/(9)\cdot x^(2)`

Which means that
`I(x) = (1)/(9)\cdot P(x)`, that is, a scale factor is applied to preimage in order to diminish growth rate of parabola at same values of x.

Some values of P(x) and I(x) are presented below:

x P(x) I(x)

0 0 0

1 1 1/9

2 4 4/9

3 9 1

The following image corresponds to both functions.

Answer 2

The picture with the widest graph in red

Explanation:

The graph P(x) is the parent graph for all quadratic functions. It has a vertex of (0,0) and has the following points:

x f(x)

-2 4

-1 1

0 0

1 1

2 4

The image of l(x) = P(1/3x) changes the points of the function to

x f(x)

-2/3 4/9

-1/3 1/9

0 0

1/3 1/9

2/3 4/9

This makes the graph much wider. The graph with the widest red graph is the graph.