Chapter 4.3, Problem 15PPE

To determine

Rule that represent the function of given ordered pairs, $\left(1,2\right),\left(2,16\right),\left(3,54\right),\left(4,128\right),\left(5,250\right)$

Answer to Problem 15PPE

The rule of the function is $y=2x^3$

Explanation of Solution

Given:

The given ordered pair is,

  $\left(1,2\right),\left(2,16\right),\left(3,54\right),\left(4,128\right),\left(5,250\right)$

First represent the given ordered pair in a tabular form.

x	1	2	3	4	5
y	2	16	53	128	250

Now, for first column

For x = 1, y = 2

It can be represented by the rule $y=2x^2,y=2x^3\text{and}y=x+1$ only.

Now, checking the rule $y=2x^2$ for second column

Put x = 2

  $\begin{array}{l}y=2x^2\\ =2\times 2^2\\ =8\end{array}$

So $y=2x^2$ is not same for second column.

Now, checking the rule $y=2x^3$ for second column

Put x = 2

  $\begin{array}{l}y=2x^3\\ =2\times 2^3\\ =16\end{array}$

So, $y=2x^3$ is same for second column.

Now, checking the rule $y=x+1$ for second column

Put x = 2

  $\begin{array}{l}y=x+1\\ =2+1\\ =3\end{array}$

So, $y=x+1$ is not same for second column.

Hence, only $y=2x^3$ rule follows for second column.

Similarly, it is same for the remaining column also.

Hence, the rule of the function for the given ordered pair is $y=2x^3$