Chapter 1Functions1.1 Relations1. A relation between two sets is
the correspondence between elements of one set, X and elements of
the other set, Y.2. The diagram shows the 'square root of' relation
between set X and set Y.3456square root ofYX91625
CodomainDomain
Domain = set X = {9, 16, 25} Codomain = set Y= {3, 4, 5, 6}
Objects = 9, 16, 25 Images = 3, 4, 5, 6Range = {3, 4, 5}3. There
are four types of relation.(a) One-to-one relationEach object in
the domain has only one image345square root ofYX91625
CodomainDomain
(b) Many-to-one relationEach image in the range has more than
one object in the domain but each object has only one image
1520
multiple ofYX345
CodomainDomain
(c) One-to-many relationEach object in the domain has more than
one image
345factor ofYX1520
CodomainDomain
(d) Many-to-many relationEach object in the domain has more than
one image and each image in the range has more than one object
152025
multiple ofYX345
CodomainDomain
1.2 Functions1. Functions are special relations where each and
every object has only one image. Hence, only one-to-one relation or
many-to-one relation are considered as functions.2. A function can
be represented by a function notation as below,(a) The function f
maps x onto y.or(b) Y is the image of x under the function f.3. The
absolute valued function is defined by
