Page 5 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

1.1 Functions

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Functions
Suppose we have set A = {1, 4, 9, 16, 25} and set B = {1, 2, 3, 4, 5}. Each element in set B is the square root
of a corresponding element in set A. Figure 1.1 shows the relation ‘is the square root of’ between the elements
in set A and set B.
A 'is the square root of' B
1 1
4 2
9 3
16 4
25 5
Figure 1.1
The relation between set A and set B can also be represented by the set of ordered pairs as follows:
{(1, 1), (4, 2), (9, 3), (16, 4), (25, 5)}
In the relation between set A and set B, each element in set A is connected to a unique element in set B. A
relation such as this is known as a one-to-one relation.

Now, suppose set P = {–2, –1, 1, 2, 3,} and set Q = {1, 4, 9, 16}. The relation between set P and set Q is as
shown in the following diagram:
P 'is the square of' Q
–2
1
–1
4
1
9
2
16
3
Figure 1.2
Notice that in the relation between set P and set Q, the elements –2 and 2 of set P are connected to the element
4 of set Q, and the elements –1 and 1 of set P are connected to the element 1 in set Q. A relation such as this
is known as a many-to-one relation.
A relation whereby each element in a set X is connected to one and only one element in a set Y is known as
a function. Hence, one-to-one relations and many-to-one relations are functions. If a relation is one-to-one,
then the function is one-to-one.
A function f from a set X to a set Y is defined as a rule that associates exactly one element of Y with each
element of X. We say, f maps X into Y and we write f : X → Y.
If x  X and y  Y such that y is assigned to x under f, we say f maps x to y and we write f : x ↦ y or y =
f(x), where y is the image of x.

In general, a function f is defined for certain values of x only. This set of values of x for which f is defined is
called the domain of f. The set of values of f(x) for a given domain is called the range of f.
In the previous example, let g be the function “is the square of’ from set P to set Q.
We write g : x ↦ x or g(x) = x .
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01a STPM Math T T1.indd 2 3/28/18 4:20 PM