Page 36 - Mathematics_Form_3

Functions

Chapter Two

Functions
FOR ONLINE READING ONLY

Introduction

A function is a special type of a relationship between the elements of two sets A
and B. It provides a way of representing real world situations mathematically,
where a specific input yields a corresponding specific output. A function can
be compared to a machine that produces a unique output based on one or
more inputs. In this chapter, you will learn the concept of a function, types
of functions, representing functions pictorially, identifying functions among
relations, drawing graphs of functions, stating the domain and range of
functions, and finding inverse functions. The competencies developed in
this chapter will enable you to represent some real life activities in terms of
functions, such as finding circumferences and areas of large objects, recording
quantities of things in related measuring units, analysing supply and demand
in terms of prices of goods, among many other applications.

Think
Scientific formulas, programming languages, Artificial Intelligence
(AI), internet, without the knowledge of functions.

Concept of a function
Some relations have special properties. For instance, consider two sets A and B,
where A is a set of children and B is the set of their mothers, as shown in Figure
2.1 and Figure 2.2.
‘ is a child of ’ In Figure 2.1, every child in set A is
A B connected to exactly one mother in set
Ibrahim Fatima B. This implies that, every child is born Mathematics for Secondary Schools
Asha to exactly one mother. This relation is
Hussein true because, in real life, a child is born
Beatrice Belina to only one mother.
Simon
Neema In Figure 2.2, some children in set A are
Shamsa Zuhura connected to more than one mother in
Rehema set B. This implies that, a child is born
to more than one mother, which is not
Figure 2.1: Pictorial representation of true in real life.
the relation “is a child of”

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