Mathematics 7th grade | UNIT 2: Sequences‚ expressions and formulae 2.3 Representing simple functions

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A function is a relationship between two sets of numbers.
A function can be shown as a function machine like this.

This function machine adds 3 to any number that goes into the machine.

The numbers that you put into the function machine are called the input.
The numbers that you get out of the function machine are called the output.
A function can also be shown as a mapping diagram like this.

Input Output

We say that 2 maps to 5, 4 maps to 7 and 5 maps to 8.

a: Find the missing inputs and outputs in this function machine.

Input Output 1 ... 3 x2 ... ... 10

b: Draw a mapping diagram to show the function in part a.

a: a Input Output 1 2 3 x2 6 5 10

To work out the outputs, multiply the inputs by 2.
$1 \times 2 = 2\,\,,\,\,3 \times 2 = 6$
To work out the input, work backwards and divide the output by 2.
$10 \div 2 = 5$
b: Input Output

1 maps to $2,3$ maps to 6 and 5 maps to 10.

1) Copy these function machines and work out the missing inputs and outputs.

2) Copy these function machines and work out the missing inputs and outputs.

$Input Output $\begin{array}{{20}{c}} {4 \to } \\ {6 \to } \\ {10 \to } \end{array} \div 2 \to + 5\begin{array}{{20}{c}} { \to ...} \\ { \to ...} \\ { \to ...} \end{array}$$ b	$Input Output $\begin{array}{{20}{c}} {2 \to } \\ {5 \to } \\ {... \to } \end{array}\,\,\,\,\, \times 2 \to \, + 1\,\begin{array}{{20}{c}} { \to 5} \\ { \to ...} \\ { \to 9} \end{array}$$ a
$Input Output $\begin{array}{{20}{c}} {6 \to } \\ {... \to } \\ {... \to } \end{array} - 4 \to \times 3\begin{array}{{20}{c}} { \to ...} \\ { \to 12} \\ { \to 24} \end{array}$$ d	$Input Output $\begin{array}{{20}{c}} {1 \to } \\ {3 \to } \\ {... \to } \end{array} + 7 \to \times 2\begin{array}{{20}{c}} { \to ...} \\ { \to ...} \\ { \to 24} \end{array}$$ c

3) a: Work out the rule to complete cach of these function machines.

Input Output $\begin{array}{*{20}{c}} {8 \to } \\ {6 \to } \\ {2 \to } \end{array}...\begin{array}{*{20}{c}} { \to 4} \\ { \to 3} \\ { \to 1} \end{array}$ — ii

b: Make two copies of the diagram below.

Input Output

Draw a mapping diagram for each of the functions in part a.

4) Tanesha and Dakarai look at this function machine.

Test the input numbers in each of their functions to see if either of them is correct.

$Input Output $\begin{array}{*{20}{c}} {2 \to } \\ {5 \to } \\ {8 \to } \end{array}... \to ...\begin{array}{*{20}{c}} { \to 2} \\ { \to 14} \\ { \to 26} \end{array}$$

I think the function is: "Multiply by 3 then take away 4.

I think the function is: "Multiply by 4 then take away 6.'

Is either of them correct? Explain your answer.

5) Chin-Mac draws this mapping diagram and function machine for the same function.

Input Output

Fill in the missing numbers and the rule in the function machine.

$Input Output $\begin{array}{{20}{c}} {4 \to } \\ {6 \to } \\ {10 \to } \end{array} \div 2 \to + 5\begin{array}{{20}{c}} { \to ...} \\ { \to ...} \\ { \to ...} \end{array}$$ b	$Input Output $\begin{array}{{20}{c}} {2 \to } \\ {5 \to } \\ {... \to } \end{array}\,\,\,\,\, \times 2 \to \, + 1\,\begin{array}{{20}{c}} { \to 5} \\ { \to ...} \\ { \to 9} \end{array}$$ a
$Input Output $\begin{array}{{20}{c}} {6 \to } \\ {... \to } \\ {... \to } \end{array} - 4 \to \times 3\begin{array}{{20}{c}} { \to ...} \\ { \to 12} \\ { \to 24} \end{array}$$ d	$Input Output $\begin{array}{{20}{c}} {1 \to } \\ {3 \to } \\ {... \to } \end{array} + 7 \to \times 2\begin{array}{{20}{c}} { \to ...} \\ { \to ...} \\ { \to 24} \end{array}$$ c

Mathematics 7th grade | UNIT 2: Sequences‚ expressions and formulae 2.3 Representing simple functions

Worked example 2.3

Exercise 2.3

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