A one-to-one function is a function where each input value is mapped to a unique output value, so that no two inputs map to the same output. A function is one-to-one if any two different inputs x1 and x2 will always produce different outputs f(x1) and f(x2). The document provides examples of relations that are and are not one-to-one functions, such as the relation between airports and their unique three-letter codes being a one-to-one function, while the relation between distance traveled on a jeepney route and fare is not one-to-one as different distances can have the same fare.

1. LESSON 9: ONE TO ONE FUNCTION

2. One To One Function
A one-to-one function is a function in which the answers
never repeat. A normal function can have two different
input values that produce the same answer, but a one-to-
one function does not.
-the function f is one-to-one if for any x1, x2 in the domain
of f, then f(x1) f(x2) , that is the same y-value is never
paired with two different x-values
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3. Example 1-5
(determined whether the given relation is a function,
if it is a function, determine whether it is one-to-one)
1. The relation pairing an SSS member to his or her SSS
number.
Solution: Each SSS member assisgned a unique SSS
number. Thus the relation is a function. Further , two
different members cannot be assigned the same SSS
number. Thus, the function is one-to-one

4. Example 2. The relation pairing a real number to its
square.
Solution: Each real number has a unique perfect
square. Thus, the relation is a function. However,
two different real numbers such as 2 and -2 may
have the same square. Thus, the function is not
one-to-one .

5. Example 3 The relation pairing an airport to its airport
code. Airport codes are three letter codes used to
uniquely identify airports around the world and
prominently displayed on checked-in bags to denote
the destination of these bags.
MNL - Ninoy Aquino International Airport (All Terminals)
CEB - Mactan - Cebu International Airport
DVO - Francisco Bangoy International Airport (Davao)
JFK - John F. Kennedy International Airport (New York City)
CDG - Charles de Gaulle International Airport
(Paris, France)
Solution:
Since each airport has a unique airport code, then the
relation is a function. Also, since no two airports share
the same airport code, then the function is one to one

6. Example 4. The relation pairing a person
to his or her citizenship.
Solution:
The relation is not a function because a
person can have dual citizenship (i.e
citizenship is not unique)

7. Example 5. The relation pairing a distance d (in
kilometers) traveled along a given jeepney route to
the jeepney fare for traveling that distance
Solution
If the distance to be traveled is 3 kms, then F(3) = 8.
However the function is not one-to-one because
different distances (e.g 2, 3,or 4 kilometers) are
changed the same rate (P8.00). That is, because F(3) =
F(2) = F(3.5)= 8, the the F is not one-to-one