Question

The function P(x) is mapped to I(x) by a dilation in the following graph. Parabola p of x passes through (negative 1.5, 0), (2, negative 3) & (5.5, 0). Parabola I of X passes through (negative 1.5, 0), (2, negative 6) & (5.5, 0).© 2018 StrongMind. Created using GeoGebra. Which answer gives the correct transformation of P(x) to get to I(x)?

Answer 1

An answer gives the correct transformation of P(x) to get to I(x) is: D. I(x) = 2P(x).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size (dimensions) of a geometric object, but not its shape.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y) → (kx, ky)

Where:

• x and y represents the data points.
• k represents the scale factor.

Since the graphs of both quadratic functions pass through the points (2, -3) for P(x) and (2, -6), we would determine the scale factor as follows;

I(x) = kP(x)

k = I(x)/P(x)

k = I(2)/P(2)

k = -6/-3

k = 2.

Answer 2

Okay, here we have this:

Considering the provided graph and transformation, we are going to identify the correct transformation of P(x) to get to I(x), so we obtain the following:

So let's remember that dilating a function by a factor of scale "" the new function to be created will be ( ) → ( ),

That is to say that the scale value will be multiplied by the value of f(x), not directly by x, so in this way we discard options a and b.

Now to calculate the scale factor, we will calculate it using the values of P and I, when x is equal to 6, we have:

I(X)=aP(x)

I(6)=aP(6)

2=a(1)

a=2/1

a=2

Therefore, we finally obtain that "a" (the scale factor) is equal to 2. Therefore, the correct transformation is: I(X)=2P(x).

Finally we got that the correct answer is the fourth option.