Function Tables with One-Step Rules

A function table has values of input and output and a function rule. In the function rule, if we plug in different values for the input, we get corresponding values of output. There is always a pattern in the way input values (x) and the output values (y) are related which is given by the function rule.

A function table is also called an input-output table. It can be drawn as a vertical table or horizontally as shown

x y
0 0
1 3
2 6
3 9

or

x 1 2 3 4 5
y 5 10 15 20 25

For example, a rule can be written as ‘add 2’ meaning add 2 to the input to get the output or it can be taken as ‘multiply by 4’ meaning multiply the input by 4 to get the output and so on.

Such rules can also be expressed using an equation as follows.

y = x + 2; y = 4x and so on.

Determine what one-step rule is used in the function table below.

In Out
15 21
18 24
21 27

Solution

Step 1:

21 = 15 + 6; 24 = 18 + 6; 27 = 21 + 6; or output = input + 6

Step 2:

So, the rule is ‘Add 6’ to input to get output.

Determine what one-step rule is used in the function table below.

In Out
13 20
16 23
19 26

Solution

Step 1:

20 = 13 + 7; 23 = 16 + 7; 26 = 19 + 7; or output = input + 7

Step 2:

So, the rule is ‘Add 7’ to input to get output.

Determine what one-step rule is used in the function table below.

In Out
35 21
38 24
41 27

Solution

Step 1:

21 = 35 − 14; 24 = 38 − 14; 27 = 41 − 14;

Step 2:

So, the rule is ‘Subtract 14’ to input to get output.

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