Question

Examine the following graph, where the function P(x) is dilated to get I(x). P of x: parabola with vertex (0, negative 8) & passes through (2, negative 4). I of x: skinnier parabola with vertex (0, negative 8) & passes through (1/2, -4).© 2018 StrongMind. Created using GeoGebra. Which answer gives the correct transformation of P(x) to get to I(x)?

Answer 1

I(x) = P(4x)

Step-by-step explanation:

We have the point (2, -4) for P(x) and the point (1/2, -4) for I(x)

So, we can see that

I(x) -----------> P(x)

(1/2, -4) -----> ( 4(1/2), -4) = (2, -4)

Therefore, I(x) = P(4x)

Because the coordinate of x in I(x) has to be multiplied by 4 to get the same coordinate of y in P(x).

For example, P(x) passes through the point (x, P(x)) = (4, 8). Then I(1) = P(4(1)) = P(4) = 8. So, I(x) passes through the point (1, 8)

Then, the correct transformation of P(x) to get I(x) is

I(x) = P(4x)