Step 1. The function P(x) that we have is:
[tex]P(x)=2x+1[/tex]
And the function that is dilated by is the function I(x) defined as follows:
[tex]I(x)=\frac{1}{2}P(x)[/tex]
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):
[tex]\begin{gathered} I(x)=\frac{1}{2}P(x) \\ \downarrow\downarrow \\ I(x)=\frac{1}{2}(2x+1) \end{gathered}[/tex]
Step 3. Now we need to simplify this expression. For that, we multiply 1/2 by 2x and by 1:
[tex]I(x)=\frac{1}{2}\cdot2x+\frac{1}{2}\cdot1[/tex]
Simplifying the multiplications:
[tex]I(x)=x+\frac{1}{2}[/tex]
That is the function rule for I(x) and it is shown in the first option.
Answer:
[tex]I(x)=x+\frac{1}{2}[/tex]
