Senior High School
Grade 11
GENERAL MATHEMATICS
(MAT 111)

CHAPTER 1: FUNCTIONS
LESSON 1: FUNCTIONS AS MODEL
Difference of relations and
functions
Relations
is a rule that relates values
from a set of values(domain)
to a second set of values
(range)
Elements of the domain can
be imagined as input to a
machine that applies a rule to
these inputs to generate one
or more outputs.
A set of ordered pairs (x, y)
Functions
is a relation where each element
in the domain is related to only
one value in the range by some
rule.
Elements of the domain can be
imagined as input to a machine
that applies a rule so that each
input corresponds to only one
output.
A set of ordered pairs (x, y) such
that no two ordered pairs have
the same x-vaue but different y-
values.

FUNCTIONS AND RELATIONS AS A TABLE OF
VALUES
•
Example 1: which of the following relations are
functions?
a.
f = {(1,2), (2,2), (3,5), (4,5)}
b.
g = {(1,3), (1,4), (2,5), (2,6), (3,7)}
c.
h = {(1,3), (2,6), (3,9) . . . , (
n,
3
n)… }
Relations f and h

•Example 2: which of the following mapping diagrams represent functions?123453591733f5678901g7211113171923h

FUNCTIONS AS A GRAPH IN THE CARTESIAN
PLANE
The Vertical Line Test
•
A graph represents a function if and
only each vertical line intersects the
graph at most once.

•Example 3: which of the following graphs can be graphs of functions?
A
B
C
D

Example 4: which of the following represents a function?•
a)y = 2x + b)y = c)x2 + y2= d)y e)y
1
1
=
=

1
1
=
=
•Identify the domain for each relation using set builder notationdomaina)[-1, 1]b)[-1, +∞]c)(-∞,1) (1, +∞)

1
1
=
=
If a relation is a function, then y can be replaced with f(x) to denote that the value of y depends on the value of x.functions
1
=
=

FUNCTIONS AS REPRESENTATIONS OF REAL-LIFE
SITUATIONS