Question

what is the function for (0,0)(1,0.5)(2,2)(3,4.5)

Answer 1

what function?

Answer 2

x = 0 gives y = 0
x = 1 gives y = 0.5
x = 2 gives y = 2
x = 3 gives y = 4.5

Notice that going from 0 to 0.5 is a jump of 0.5
Going from 0.5 to 2 is a jump of 1.5
Going from 2 to 4.5 is a jump of 2.5

So the pattern should indicate that you do: \(0 \rightarrow +0.5 \rightarrow +1.5 \rightarrow + 2.5 \rightarrow \ldots \)
Or another way to see it which might be easier is to see (and write as a function) that you are doing:
\(x = 0, y = 0^2(0.5)=0\\
x = 1, y = 1^2(0.5)=0.5\\
x =2, y = 2^2(0.5)=2\)
etc.