Page 23 - Mathematics_Form_3

Relations

12. The range is obtained by writing x in
terms of y and determine the possible
y
real values of for which x is defined,

4 that is, y = 2x + 1, which implies that
y=x +4x+3 y=x+3
2
FOR ONLINE READING ONLY
3 y − 1
x = _____ .

2
2 2 y − 1
_
From x = , it is observed that any
1 2
real value of y gives a definite real value
of x . Hence, the range of y = 2x + 1 is
-4 -3 -2 -1 0 1 2 x
also the set of all real numbers.
-1

Example 1.16
Find the domain and range of the
2
relation y = 3 x + 2.
Domain and range of a relation
expressed in equation form Solution
When a relation is written in the form of All values of x give definite values of
2
an equation, say y = 2x + 1, the domain y. Thus, the domain of y = 3 x + 2
of the relation is the set of all possible is the set of all real numbers, that is,
input values of the independent variable domain = {x : x ∈ ℝ} .
x. When these values are substituted For the range, first write x in terms of
into the relation they give values of the y, that is, from 2 _
y = 3 x + 2,

dependent variable y. On the other hand,
Mathematics for Secondary Schools values y of the relation. The values in the square root are defined
making x the subject gives
range is the set of all possible output
y − 2
_

x = ± .
√ 3

Example 1.15
only for the non-negative real numbers.
It gives,
Find the domain and range of the
y − 2
relation y = 2x + 1.
_
≥ 0,

3
Solution
y ≥ 2.
Given the relation y = 2x + 1, any real
value of x gives a definite real value Thus, the range = {y : y ≥ 2} .
of y. Therefore, the domain of this Therefore, the domain = {x : x ∈ ℝ}

relation is the set of all real numbers. and range = {y : y ≥ 2} .
16 Student\s Book Form Three

18/09/2025 09:58:42
MATHEMATIC F3 SB.indd 16 18/09/2025 09:58:42
MATHEMATIC F3 SB.indd 16