Chapter 4.3, Problem 16PPE

To determine

Rule that represent the function of given ordered pairs, $\left(0,0\right),\left(1,0.5\right),\left(2,2\right),\left(3,4.5\right),\left(4,8\right)$

Answer to Problem 16PPE

The rule of the function is $y=\frac{x^2}{2}$

Explanation of Solution

Given:

The given ordered pair is,

  $\left(0,0\right),\left(1,0.5\right),\left(2,2\right),\left(3,4.5\right),\left(4,8\right)$

First represent the given ordered pair in a tabular form.

x	0	1	2	3	4
y	0	0.5	2	4.5	8

Now, for first column

For x = 0, y = 0

It can be represented by many rules.

Now, for second column

For x = 1, y = 0.5

It can be represented by the rule $y=\frac{x^2}{2}$ only.

So, checking this rule for third column.

Put x = 2

  $\begin{array}{l}y=\frac{x^2}{2}\\ =\frac{2^2}{2}\\ =2\end{array}$

So it is same for third column.

Similarly, it is same for the remaining column also.

Hence, the rule of the function for the given ordered pair is $y=\frac{x^2}{2}$