Page 33 - Mathematics_Form_3

Relations

14. Revision exercise 1

y In questions 1 to 4, use {1, 2, 3, 4} as
4 the domain of the relation to give the
y=|x|
3 range of each of the given mappings:
FOR ONLINE READING ONLY
y=2
2 1. R : x ↦ 2x .
1 2. R : x ↦ 3x − 7 .

-3 -2 -1 0 1 2 3 x 3. R : x ↦ 4x + 5 .
-1
4. R : x ↦ x .
2
-2
5. If X = {4, 3, 8} and Y = {a, 1} ,
list the ordered pairs of the following
relations:

Chapter summary ( a ) X → Y .
1. A relation between two sets A and B ( b ) Y → X .
is a set of ordered pairs (x, y), with
x ∈ A and y ∈ B. A relation can be ( c ) X → X .
represented by a pictorial diagram. ( d ) Y → Y .

2. Given R : A → B, the domain of 6. Represent the following relations
R is the set of elements of set A in the -plane:
which occur in the relation. The
range is the set of members of set ( a ) R = {(3, 2 ), (2, 2)} .
B that are paired with elements of ( b ) R = {1, 2 ), (1, 5 ), (1, 7 ),
Mathematics for Secondary Schools 4. An equation in x and y is a relation. 7. Represent each of the following
set A in the relation.
(3, 5 ), (2, 2 ), (2, 7)} .
3. A relation between sets of numbers
can be represented using a graph.
(c) R = {(2, 4 ), (2, 3 ), (7, 1 ),
(5, 4)} .
It can be represented by a graph.
5. An inequality in x and y is a
relations by using arrow diagrams:
relation. It can be represented by
a shaded region.
( a ) R = {(3, 2 ), (2, 2)} .
6. The inverse of a relation R
between sets A and B is found
by interchanging the elements in
(3, 5 ), (2, 2 ), (2, 7)}
the relation R. On a graph, it is (b) R = {(1, 2 ), (1, 5 ), (1, 7 ),
(c) R = {(2, 4 ), (2, 3 ), (7, 1 ),
shown by interchanging the x and
y coordinates. (5, 4)}.

26 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 26