table of ordered pairs

Introduction

In this lesson, we find the function rule given a table of ordered pairs.

We first identify the input and the output variables and their values. We find if the function is increasing or decreasing.

If the function is increasing, it means there is either an addition or multiplication operation between the two variables.

If the function is decreasing, it means there is either a subtraction or division operation between the two variables.

Consider the following table −

x	y
3	15
5	25
6	30
8	40
9	45

We see that the y values are increasing as the x values are increasing. So it is an increasing function. So, the variables x and y must be related either by addition or multiplication operation.

We check addition operation on x and y values as follows −

3 + 12 = 15

5 + 12 = 17

We check multiplication operation on x and y values as follows −

3 x 5 = 15

5 x 5 = 25 and so on

We see that the relation between x and y is a multiplication operation here and the constant for which all values are satisfied is 5.

So the function rule for this table of x and y values is Multiply by 5.

Consider another table −

x	y
10	13
15	18
19	22
23	26
28	31

Here we identify the input and output and then see the output y is increasing as input x is increasing.

13 = 10 + 3; 18 = 15 + 3; 22 = 19 + 3 and so on.

So, output y = input x + 3

Therefore, we identify the function rule here as Add 3.

Example 1

Given the following table of ordered pairs, write a one-step function rule.

Inputx	Outputy
0	3
2	5
4	7
6	9
8	11

Solution

Step 1:

From the table 0 + 3 = 3; 2 + 3 = 5 and so on

Step 2:

Input + 3 = Output or x + 3 = y

Step 3:

Therefore the function rule here is Add 3 to the input to get the output.

Example 2

Given the following table of ordered pairs, write a one-step function rule.

Inputx	Outputy
0	0
1	6
2	12
3	18
4	24

Solution

Step 1:

From the table 0 × 6 = 0; 1 × 6 = 6 and so on

Step 2:

Input × 6 = Output or x × 6 = y

Step 3:

Therefore the function rule here is Multiply by 6 the input to get the output.