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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