Cambridge Additional Mathematics

(singke) #1
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

4037 Cambridge
cyan magenta yellow black Additional Mathematics

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_02\039CamAdd_02.cdr Thursday, 3 April 2014 4:03:18 PM BRIAN

Free download pdf