Question

The function P(x)=x3−2x2 is dilated by the function I(x)=P(4x).

Which function rule represents I(x)?

I(x)=64x3−2x2

I(x)=4x3−2x2

I(x)=64x3−32x2

I(x)=4x3−8x2

Answer 1

I(x) = 64x³−32x²

Explanation:

We are given the function P(x)=x³−2x².

I(x) is given P(4x).

This means to get I(x), we replace x in the function P(x) to be 4x.

Therefore:

I(x) = P(4x) = (4x)³−2(4x)²

I(x) = P(4x) = 64x³ - 2(16x²)

I(x) = 64x³ - 32x²

Therefore the function rule that represents I(x) is 64x³ - 32x².