Page 31 - Mathematics_Form_3

Relations

−1

4 y R = {(1, − 2), (− 1, − 2), (−1, 0), (0, 2),
(0, − 2), (1, 0), (−1, 0), (1, 2)} .
3
The graph of R is as shown in the
−1
2 y=x
following figure.
1
FOR ONLINE READING ONLY
x y
-4 -3 -2 -1 0 1 2 3 4 3
-1 (-1, 2) (1, 2)
2
-2
x=0
-3 1
-4 x
-3 -2 -1 0 1 2 3
From the graph, it can be observed that -1

the domain of R = {x : x ≤ 0} and
−1
−1
the range of R = {y : y ≤ 0} . -2
(-1, -2) (1, -2)
-3
Example 1.29
From the graph, the domain of
Draw the graph of the inverse of the R = {x : − 1 ≤ x ≤ 1} and the range
−1
relation R shown in the following
−1
of R = {y : − 2 ≤ y ≤ 2} .
figure. Use the graph to find the domain
and range of the inverse relation.

y Exercise 1.8
2
In questions 1 to 8, draw the graph
(-2, 1)
(2, 1)
Mathematics for Secondary Schools Solution -1 (2,-1) range of each inverse relation.
1
of the inverse of each of the given
relations, hence find the domain and
x
-1
0
-3
-2
2
3
1
(-2,-1)
1. R = {(x, y ): y = 2x − 2} .
-2
2
2. R = {(x, y ) : y = x } .
From the figure the coordinates of the
points on the boundary of the relation
R, are R = {(− 2, 1), (− 2, − 1), (0, − 1),
4. R = {(x, y ) : x > 0} .
(2, 0), (− 2, 0), (0, 1), (0, − 1), (2, 1)} . 3. R = {(x, y ) : 2y − x = 4} .
Interchanging the coordinates gives 5. R = {(x, y ) : 2y > x} .

24 Student\s Book Form Three

18/09/2025 09:58:46
MATHEMATIC F3 SB.indd 24 18/09/2025 09:58:46
MATHEMATIC F3 SB.indd 24