This document discusses relations and functions in mathematics. It provides definitions of both relations and functions, noting that a function is a special type of relation where each input is mapped to only one output. The key differences between relations and functions are explained, including that relations can have a one-to-many or many-to-one relationship while functions must have a one-to-one relationship. Examples of graphs of functions and relations are given, showing that a vertical line test will pass through a function graph only once but may pass through a relation graph multiple times.

1. Nathalie Maria P.
Emeterio
TRUE OR FALSE. A
function is a special
type of relation.
Is the graph below a
function or a relation?
REFERENCES
RELATIONS
AND
FUNCTIONS
TEST YOURSELF
Congratulations!
You now know
more about
relations and
functions!
Admin. (2022, August 24). Relations and
Functions - definition, types, and
examples. BYJUS.
https://byjus.com/maths/relations-and-
functions/
Admin. (2023, August 29). Functions -
definition, types, domain range and video
lesson. BYJUS.
https://byjus.com/jee/functions-and-its-
types//
Libretexts. (2023, June 4). 2.1: Relations
and functions. Mathematics LibreTexts.
https://math.libretexts.org/Courses/Kansa
s_State_University/Your_Guide_to_Interme
diate_Algebra/02%3A_Introduction_to_Fu
nctions_and_Graphing/2.01%3A_Relations_
and_functions
Relations and Functions - definition,
difference, types, examples. (n.d.).
Cuemath.
https://www.cuemath.com/algebra/relatio
ns-and-functions/
Team, T., USA. (2023, October 19). Relations
and Functions: Definition, Types, and
examples - Turito. US Learn.
https://www.turito.com/learn/math/relatio
ns-and-function
1
2
What is the mathematical
rule that all functions
should follow?
3

2. Graph of a Function.
A vertical line test will pass
through the graph only once.
Functions are also set of ordered
pairs just like relations, but every
input shall be associated with
only one output.
VERTICAL LINE
TEST THEOREM
WHAT’S THE MAIN
DIFFERENCE?
Relations show a one-to-
many or many-to-one
relationship, while functions
show a one-to-one
relationship.
1
2
RELATIONS
FUNCTIONS
A function is a relation
which describes that
there should be only
one output for each
input (or) that follows
the rule:
i.e., every X-value
should be
associated with
only one y-value is
called a function.
A mathematical relation is
a bunch of points
(ordered pairs). In other
words, the relation
between the two sets is
defined as the collection
of the ordered pair, in
which the ordered pair is
formed by the object from
each set.
FUNCTION RELATION
A set of points in the
Cartesian plane is the
graph of a function if and
only if every vertical line
intersects the graph in at
most one point.
Graph of a Relation.
A vertical line test will pass through
the graph more than once.