Question

The function P(x)=2x+1 is dilated by the function I(x)=12P(x).Which function rule represents I(x)?

Answer 1

I(x)=x+1

Explanation:

Answer 2

Step 1. The function P(x) that we have is:

`P(x)=2x+1`

And the function that is dilated by is the function I(x) defined as follows:

`I(x)=(1)/(2)P(x)`

This means that we will be dilating the original function P(x) by 1/2.

Step 2. To find the function rule that represents I(x), we need to substitute P(x) into I(x):

`\begin{gathered} I(x)=(1)/(2)P(x) \\ \downarrow\downarrow \\ I(x)=(1)/(2)(2x+1) \end{gathered}`

Step 3. Now we need to simplify this expression. For that, we multiply 1/2 by 2x and by 1:

`I(x)=(1)/(2)\cdot2x+(1)/(2)\cdot1`

Simplifying the multiplications:

`I(x)=x+(1)/(2)`

That is the function rule for I(x) and it is shown in the first option.

Answer:

`I(x)=x+(1)/(2)`