Question

the ordered pairs (0, 0), (1, 0.5), (2, 2), (3, 4.5) and (4, 8) represent a function. What is a rule that represents this function?

Answer 1

Answer:

The rule that represents function is $y=\frac{1}{2} x^2$.

Step-by-step explanation:

Given ordered pairs  (0, 0), (1, 0.5), (2, 2), (3, 4.5) and (4, 8) 0r we can write $(0,0)$, $(1, \frac{1}{2})$, $(2,2)$, $(3,\frac{9}{2})$ and $(4,8)$.

To find the rule of the function, it is important to find any invariant value for any x-values.

For this case we can see that if we square each value of x and then multiply by $\frac{1}{2}$, we get the corresponding values of y, i.e,

$\frac{1}{2}\cdot (0)^2$$=0$

$\frac{1}{2}\cdot (1)^2=\frac{1}{2}$

$\frac{1}{2}\cdot (2)^2=\frac{1}{2}\cdot 4=2$

$\frac{1}{2}\cdot (3)^2=\frac{1}{2}\cdot 9=\frac{9}{2} =4.5$

$\frac{1}{2}\cdot (4)^2=\frac{1}{2}\cdot 16=8$

As you can see above , the rule of function follows above is, $y=\frac{1}{2} x^2$