Page 6 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions

A Explaining functions using graphical 1
representations and function The following arrow diagram shows the relationship
notations
between two sets X and Y.
(a) (b)
1. Assuming the price of a movie ticket is RM10.
Hence, the amount paid depends on the number Plus 1
of tickets purchased. 1 2 a 1
For example, 1 → 10, 2 → 20, 3 → 30 and Bhd. All Rights Reserved.
(a) The relationship between the number of 2 3 4 b c 4 5
tickets purchased and the total amount paid 3 5
can be represented in a graphical form as
follows. Set X Set Y Set X Set Y
(c) (d)
Squares Form 4
50 1 1 1 a
40 2 2 b
–2 4 3 c
30
Set Y 4
20
Set X Set Y Set X Set Y
10
Determine whether the relations are functions. Give
0 1 2 3 4 5 reasons for your answers.
Set X Solution
(a) Function. Each object has only one image even
(b) Note that each movie ticket purchased though element 5 does not have an object.
(input value) in set X is mapped to one and (b) Not a function. Object c has two images, which
Penerbitan Pelangi Sdn
only one price (output value) in set Y. are 4 and 5.
(c) Function. Each object has only one image even
so on. though elements 2 and –2 have the same image.
This type of relation is known as function. (d) Not a function. Element 3 does not have an
image.
(c) If f denotes a function which maps set X to
set Y, then the function can be represented SPM Tips
by the following arrow diagram. There are two types of relations which can be considered
as functions.
f
x y Capital
1 10 Pahang Kuantan
2 20 Perlis Kota Bharu
3 30
4 40 Kelantan Kangar
Set X Set Y One-to-one relation
Material class
(d) Element 1 in set X is known as the object Steel
while element 10 in set Y is known as the Copper Metal
image of 1. The same applies for 20, 30, and Wood
40, which are the images of objects 2, 3, and Plastic Non-metal
4 respectively.
Many-to-one relation

Try Questions 1 – 2 in ‘Try This! 1.1’

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