GENERAL MATHEMATICS
FUNCTIONS & RELATIONS
OBJECTIVES
 The learners will able to distinguish functions and
relations.
 The learners will able to familiarize in different ways of
representing functions.
 The learners will able to appreciate the importance of
function in real-life situations.
RELATIONS
It is a subset of the Cartesian product. Or simply, a bunch of
points (ordered pairs). In other words, the relation between the
two sets is defined as the collection of the ordered pair, in
which the ordered pair is formed by the object from each set.
Any set of ordered pairs. The set of all the first coordinates
is called Domain of the relation. The set of all second
coordinate is called Range.
RELATIONS
Note: Don’t consider duplicates while writing the
domain and range and also write it in increasing
order.
Example 1: {(1,3), (1,2), (0,8),(9,3)}
Solution: this set of ordered pair is an example of relations, wherein the
domain {0,1,9} and the range is {2,3,8}.
Example 2: {(1,4), (2,5), (3,6)}
Solution: this set of ordered pair is an example of relations, wherein the
domain {1,2,3} and the range is {4,5,6}.
Example 3: {1,2,5,7}
Solution: this is not an example of relation, because this is not a set of
ordered pairs
Example 4: {(2,3), (2,5)}
Solution: this is not an example of relation , but just a set of pairs of set.
FUNCTIONS
 A relation in which every first element x, there corresponds a unique
second element y.
A function can be denoted by y=f(x) , which reads “f of x” or “the value of the
function x”.
Note: every Function is a relation, but relations are
not function”.
5 DIFFERENT WAYS IN PRESENTING A
FUNCTIONS
1. function in ordered pair.
f(x)= {(1,6), (2,7),(3,8),(4,9),(5,10)}
2. function in tabular form
x
1
2
3
4
5
y
6
7
8
9
10
3. Function in set notation/ open
sentence
f(x)= {(x,y) I y=x+5 and x={1,2,3,4,5}
5 DIFFERENT WAYS IN PRESENTING A
FUNCTIONS
4. Arrow diagram /mapping
Note:
X
Y
1
6
One to one correspondence - one number in x is
paired with different numbers in y.
2
7
3
8
4
9
5
10
Many to one correspondence – many (more than
1) numbers in x pair with same number in y.
One to many correspondence - one number in x is
paired with different numbers in y
Hence, one to one correspondence and many to
one correspondence is considered function.
5 DIFFERENT WAYS IN PRESENTING A
FUNCTIONS
5. Graphical Form
x f(x)
0 2
2
2
Note:
A graph represent a function
if and only if each vertical line
intersects the graph at
exactly one point.
TRY THIS
Directions: Determine which of the following relations is a functions. State
the domain and range of each relation.
1. {(4,10),(2,8), (4,-7)}
2. {(1,4),(-7,3), (-1,2), (8,4)}
3. {(6,-1), (-7,5),(8,-1),( -2,0)}
4. {(0,0),(1,1),(2,2)}
5. {(6,9),(4,8),(4,-3)}
TRY THIS
Abstraction:
1. What is the difference of functions and relations?
2. What are the different ways in representing functions?
3. What are the importance of functions and relations in real- life
situations?
QUIZ
Directions: Graph the relation represented by each of the following and tell
whether the relation is a function or not.
1. {(-3,3), (-2,2), (-1,1), (0,0), (1,1), (2,2), (3,3)}
2. {(0,4), (3,3), (4,2), (3,-5), (4,-4), (0,-6)}
3. {(0,1), (1,2), (2,4), (3,8), (4,16)}
4. {(4,8), (3,4), (1,1), (-1,1), (-2,2)}
5. {(5,3), (5,-3), (0,2), (0,-2), (3,1), (3,-1), (4.0)}
EXERCISE
Directions: determine if the following represents a function.
1. n= {(4,2); (0,9), (-4,8), (4,5), (-1,10)}
2. s={(mathematics, science), ( mathematics, English), (mathematics
economics)}
3. f(x)= x