What is a Function Table?
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What is a function table?

Are there different types of function tables?

What sort of function tables questions are there?

Have you got any function table worksheets for me to try?

How do I answer function table questions?

Where can I find some examples of different function tables?

Find out more below.

What is a Function Table?

function machine image

A function table is a way of showing how a set of inputs is related to a set of outputs.

Function tables are often used to generate a set of outputs from a set of inputs following a given rule.

They can also be used to find an input from an output, or to find a rule for a given set of inputs and outputs.

In fact, function tables are sometimes called input and output tables, or function machines.

Function machines can be very simple and easy for quite young children to understand; they can also be incredibly complex and used at a much higher level for college students.

They are a great way to explore algebra and also to learn about inverse of an expression.

Here is an example of a simple in and out function table.

example of a function table 2 image

We can see that the rule for the function is subtract 3.

We can see that each output is 3 less than the corresponding input.

If we wanted to write this using algebra, we could say that:

  • y = x − 3
  • f(x) = x − 3

for any input x.

Are there different types of function table?

All function tables are based around inputs and outputs.

The headings on some tables may be different, for example you might get x and y, or you might get x and f(x).

But these other headings are just a different way of having inputs and outputs.

The main differences in function tables are the types of function.

Here are some examples of some of the function types you might get in a table:

Functions with rules rather than algebraic expressions:

  • simple one-step rules: add 4, subtract 1, multiply by 5, etc
  • two-step functions: add 3 then double, halve it then subtract 2, etc

Algebraic functions:

  • linear functions of the form f(x) = mx + c for some numbers m and c.
  • quadratic functions where the value of x has an exponent of 2, such as f(x) = x2 + 4
  • other functions where you might have different exponents or other mathematical operators.

What sort of function table questions are there?

Function table questions fall into 3 different categories:

  • finding the output if we know the input and the rule (or function).
  • finding the input if we know the output and the rule (or function).
  • finding the rule or function if both the inputs and outputs are known.

We have created a range of different worksheets for you to practice all these skills.

How do I answer Function Table questions?

We have created a support page to help you to answer a range of questions involving function tables.

Each of the three different types of question above are included in our worked examples which are solved step-by-step.

how to do function tables image

Have you got some function table worksheets for me to try?

We have a range of function table worksheets from 3rd grade and upwards.

The worksheets involve finding missing inputs and outputs, as well as finding the missing function.

The easier worksheets involve using rules rather than algebraic functions; the harder worksheets use algebraic functions.

The harder worksheets are more suitable for middle and high school level.

input output tables worksheet image input and output function tables worksheets image

What is a Function Table - Some Examples

Here are some examples of different function tables to show you what is a function table and how they work.

1) Example of a one-step rule in a table.

example of a function table 3 image

We can see that the rule is Multiply by 2.

This is a one-step function as only one operator is used.

Looking at the rows of the table, we can see:

  • when the input is 3, the output is 3 x 2 = 6
  • when the input is 2, the output is 2 x 2 = 4
  • when the input is 0, the output is 0 x 2 = 0
  • when the input is 4, the output is 4 x 2 = 8
  • when the input is 5, the output is 5 x 2 = 10.

2) Example of a two-step rule in a table.

example of a function table 4 image

We can see that the rule is Subtract 4 then divide by 3.

This is a two-step function as two different operators are used.

The function table has been set out horizontally with the input and output in rows rather than columns.

Looking at the columns of the table, we can see:

  • when the input is 16, the output is 16 − 4 = 12; 12 ÷ 3 = 4
  • when the input is 25, the output is 25 − 4 = 21; 21 ÷ 3 = 7
  • when the input is 10, the output is 10 − 4 = 6; 6 ÷ 3 = 2
  • when the input is 40, the output is 40 − 4 = 36; 36 ÷ 3 = 12
  • when the input is 49, the output is 49 − 4 = 45; 45 ÷ 3 = 15

If we were to rewrite this rule using algebra, we could write any of the following for the input, x:

  • \[ y = (x - 4) \div 3 \]
  • \[ y = {1 \over 3} (x - 4) \]
  • \[ f(x) = {{x - 4} \over 3} \]

3) Example of a one-step function in a table.

example of a function table 5 image

We can see that the rule is \[ f(x) = {1 \over 2} x \].

We could also write the rule as \[ f(x) = { x \over 2} \]

This is a one-step function as just one operator is used.

We can also see that the inputs start at 0 and count up by ones to 5. This is common in function tables, especially when using the tables for graphing the function.

Looking at the columns of the table, we can see:

  • when the input is 0, the output is half of 0 = 0.
  • when the input is 1, the output is half of 1 = ½
  • when the input is 2, the output is half of 2 = 1
  • when the input is 3, the output is half of 3 = 1 ½

If we were to rewrite this equation as a rule, then the rule would be either:

  • Halve it
  • Divide by 2

4) Another example of a one-step function in a table.

example of a function table 7 image

We can see that the rule is \[ f(x) = 20 - x \].

This is a one-step function as just one operator is used.

You will notice that the inputs to this table include fractions, and that the answers included negative numbers.

Looking at the columns of the table, we can see:

  • when the input is 16, the output is 20 − 16 = 4.
  • when the input is 3, the output is 20 − 3 = 17
  • when the input is 11, the output is 20 − 11 = 9
  • when the input is 5 ½ , the output is 20 − 5 ½ = 14 ½
  • when the input is 8 ½ , the output is 20 − 8 ½ = 11 ½
  • when the input is 22, the output is 20 − 22 = -2

If we were to rewrite this equation as a rule, then the rule would be:

  • Subctract the number from 20

5) Example of a two-step function in a table.

example of a function table 6 image

We can see that the rule is \[ f(x) = 2x + 1 \].

This is a two-step function as two operators are used.

You will notice that the inputs to this table include fractions, and that the answers included negative numbers.

Looking at the columns of the table, we can see:

  • when the input is 0, the output is (2 x 0) + 1 = 1.
  • when the input is 1, the output is (2 x 1) + 1 = 3
  • when the input is 2, the output is (2 x 2) + 1 = 5
  • when the input is 3, the output is (2 x 3) + 1 = 7
  • when the input is 4, the output is (2 x 4) + 1 = 9
  • when the input is 5, the output is (2 x 5) + 1 = 11

If we were to rewrite this equation as a rule, then the rule would be either:

  • double then add 1
  • multiply by 2 then add 1

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6th Grade Algebra Worksheets

If you are looking for some 6th grade algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

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