Page 26 - MAT KS3 Y8 Cambridge CheckPoint

2.4 Using functions and mappings

2.4 Using functions and mappings

A function is a relationship between two sets of numbers.
You can draw a function as a function machine, like this. The numbers that go into the function
machine are called the input.
Input Output
2 7 The numbers that come out of the
4 + 5 9 function machine are called the output.
5 10

You can also draw a function as a mapping diagram, like this.
Input 01 23456789 10

Output 0 1 23456789 10
The input numbers map to the output numbers.
You can write a function algebraically as an equation.
Use the letter x to represent the input numbers.
Use the letter y to represent the output numbers. x + 5 y
You can then show the function machine above like this.
x 2 4 5
You can write the input (x) and output (y) numbers in a table. y 7 9 10

You can also write the function as an equation like this: x + 5 = y
You usually write a function
but it is more common to write the equation like this: y = x + 5 equation starting with y = …

Worked example 2.4
a Copy and complete the table of values for this function machine.
x 1 2 3 4
x × 2 + 1 y y

b Draw a mapping diagram to show the function in part a.
c Write the function in part a as an equation.

a x 1 2 3 4 To work out the y-values, multiply the x-values by 2 then add 1.
1 × 2 + 1 = 3, 2 × 2 + 1 = 5, 3 × 2 + 1 = 7, 4 × 2 + 1 = 9
y 3 5 7 9

b x 01 23456789 10 Draw a line connecting each x-value to its y-value.
Draw an arrow on each line to show that 1 maps to 3, 2 maps to 5, 3
maps to 7 and 4 maps to 9.
y 0 1 23456789 10
c y = 2x + 1 Write the equation with the ‘y =’ on the left.
Remember that you can write 2 × x + 1 simply as 2x + 1.

24 2 Sequences, expressions and formulae