Answer
The function for this relation is y=0.5$x^{2}$.
The graph of this is shown in the screenshot below.
Work Step by Step
The function for the relation (0, 0), (1, 0.5), (2, 2), (3, 4.5), (4, 8) was created by taking the first difference of the y values and then the second difference of the first difference. if the second difference is equal across the x values, then the function is quadratic.
So to find the equation of the function we know since it is quadratic we can write y=a$x^{2}$.
To find a we can plug in one of the values (1,0.5),
0.5 = a($1)^{2}$
a= 0.5
(2,2)
2 = a($2)^{2}$
2=4a
a=$\frac{2}{4}$ = 0.5
Therefore y=0.5$x^{2}$
