Page 25 - Mathematics_Form_3

Relations

3. Let R = {(x, y ) : x + y = 1} be a 1. Choose a currency of any country
2
2
relation on the set of real numbers. and find its current exchange rate
(a) From the following set of pairs against the Tanzanian currency.
of numbers, write a subset 2. Express mathematically the
whose members belong to R. relationships between quantities
FOR ONLINE READING ONLY
_ in task 1 by using an equation.
(0, − 1), (1, 1), (2, − √ 3 ) , (0, 1 ), Write the relation in such a way
{
_ _ _ _ that Tanzanian currency forms the
√ 2
√ 2 √ 2
1 _ √ 3 _ _ _ _
_
, .

) (
( , , √ 2 , , 2 )} domain and foreign currency forms
) (
2 2
2
2
the range.
(b) Give the domain of the set
3. Prepare a table of values with 10
obtained in (a).
values of the domain and range
(c) Give the range of the set depending on your choice of foreign
obtained in (a). currency.
4. Find the range of the following 4. Prepare a new table and exchange
the values of the columns of the
mappings if the domain of each
table prepared in task 3.
relation is the set of integers.
5. Use the values obtained in task 4
( a ) R : x ↦ 2x − 1
to form a new equation.
2
( b ) R : x ↦ x
6. Compare the new equation with the
3
( c ) R : x ↦ x
one formed in task 2 and note down
5. Find the domain and range of the any similarities and differences.
following relations: 7. Choose some values of the range
(a) y = x + 3 from the table in task 3 and
2
(b) y = 4x substitute into the new equation.
2
What values do you get and how
Mathematics for Secondary Schools have counterparts that reverse their 8. Without using a table of values,
are they related to those in the table
Inverse of a relation
prepared in task 3? Comment on the
In our daily activities, many operations
observations.
effects.
use the equation formed in task 2
Engage in Activity 1.2 to recognise
to obtain the equation formed in
yourself with an inverse of a relation
task 5.
9. Based on your observations in task
Activity 1.2: Recognising an inverse
7, what is the new equation referred
of a relation
to in reference to the equation in
task 2?
Currencies of different countries relate
10. Share your findings to the rest of
linearly depending on a given exchange
the class members for more inputs
rate between the currencies. Perform the
and discussion.
following tasks:
18 Student\s Book Form Three

18/09/2025 09:58:43
MATHEMATIC F3 SB.indd 18
MATHEMATIC F3 SB.indd 18 18/09/2025 09:58:43