Cambridge Additional Mathematics

Functions (Chapter 2) 39

ONE-ONE FUNCTIONS

Aone-one functionis a function in which no two different ordered pairs

have the samey-coordinate or second component.

For example:

²

The function y =3x+1 is

one-one, since each distinct point

on the graph has a different

y-coordinate.

²

The function y = x^2 is not

one-one, since the graph contains

distinct points(¡ 3 ,9)and(3,9)

which have the samey-coordinate.

We can use thehorizontal line testto determine whether a function is one-one:

Suppose we draw all possible horizontal lines on the graph of a function.

² If each line cuts the graph at most once, then the function is one-one.

² If at least one line cuts the graph more than once, then the function isnotone-one.

Example 2 Self Tutor

Which of the following relations are one-one?

ab c

ab c

One-one is read

as “one to one”.

y

x

1

y=3x+1

O

y

x

(-3 9), (3 9),

y=x 2

O

y

O x

y

x

O

y

O x

one-one

y

O x

one-one

y

x

O

not one-one

y

O x

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