introduction to function( general mathematics)

• Define a function
• Represents a function through set of
ordered pairs, diagrams and graphs.
• Identify domain and range
• Representing real-life situations using
functions, including piecewise function

DANIEL
ENRIQUE
RONNIE
KATHRYN
LIZA
LOISA
GERALD
BEA
JULIA
MAJA
KIM
Function Not a function/
Relation

The 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(range).
A relation is also a set
of ordered pairs (x, y)
The 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 (range).
Set of ordered pairs (x,
y) such that no two
ordered pairs have the
same x –value but
different y - values

FUNCTION RULE
(Rule of Correspondence)
The area A of a circle is a function of its radius r. 𝐴 = 𝜋𝑟2
Domain Range
All radii r All areas A
𝑨 = 𝝅𝒓𝟐
However, different elements in the set of inputs may produce the same
elements in the set of outputs.

• Functions are often denoted by any
letter of the English alphabet or Greek
character. The most commonly used
notations are f, g, h, F, G, H, 𝜃.
• If 𝑓 is a function and 𝑥 is an element in
its domain then it is denoted by 𝑓(𝑥)

Which of the following sets of ordered pairs are functions?
X = {(1, 1), (2, 2), (3, 3), (4, 4)}
Z= {(-1, 2), (-2, 3), (1, 4), (2, 4)}
Y= {(1, 3), (1, 4), (2, 5), (2, 6), (3, 7)}
Function
Not a Function
Function
A = {(1, 0), (0, 1), (-1, 0), (0, -1)} Not a Function

1
2
3
4
5
3
5
9
11
13
x y
-2
-1
0
1
2
0
-1
4
5
-1
-2
-3
-4
x x y
y
Function Function Not a Function
A B C

Vertical line test
* A graph represents a function if and only if each vertical line
intersects the graph at most once

Not a Function
Function
Not a Function

Domain – set of inputs
- set of all
possible values that
variable x can take
- independent
variable x
Range – set of outputs
- dependent
variable y

A = {(2, 5), (-4, 7), (6, 8)}
Domain: {2, -4, 6}
Range: {5, 7, 8}

Domain: {1, 2, 3, 4, 5}
Range: {3, 5, 9, 11, 13}

𝑦 = 𝑥
Domain: 𝑥 𝑥 ∈ 𝑅} Range: 𝑦 𝑦 ∈ 𝑅}
𝑥 -1 0 1
𝑦 -1 0 1
Table of Values

𝑦 = 𝑥2
𝑥 -2 0 2
𝑦 4 0 4
Table of Values
Domain: 𝑥 𝑥 ∈ 𝑅} Range: 𝑦 𝑦 ≥ 0}

𝑦 =
1
𝑥
𝑥 -1 0 2
𝑦 -1 undefined 0.5
Table of Values
Domain: 𝑥 𝑥 ≠ 0} Range: 𝑦 𝑦 ≠ 0}

1. Give a function 𝐶 that can represent the cost of
buying 𝑥 meals, if one meals costs 40 pesos .
Solution: Since each meal cost 40 pesos, then the cost
function is 𝐶 𝑥 = 40𝑥
𝐶 3 = 40 3 = 120

2. Maya has an internet service that currently has a monthly access
fee of $11.95 and a connection fee of $0.50 per hour. Represent her
monthly cost as a function of connection time.
Let 𝑥 = the number of hours Maya spends on the internet in one month.
𝑓(𝑥) = Maya’s monthly cost
Function Rule: 𝑓 𝑥 = 11.95 + 0.50𝑥
𝑓 500 = 11.95 + 0.50 500 = $261.95

3. What if your bank charges a monthly fee of $15 for your
checking account and also charges $0.10 for each check
written? How would you represent this scenario with
a function?
Function Rule: 𝑓 𝑥 = 15 + 0.10𝑥

A videoke machine can be rented for 1000 pesos for three days, but for the
fourth day onwards, and additional cost of 400 pesos per day is added.
Represent the cost of renting a videoke machine as a piecewise function of
the number of days it is rented.
Let 𝑥 = number of days
1000 If 0 ≤ 𝑥 ≤ 3
1000 + 400(𝑥 − 3) if 𝑥 > 3
𝑓 𝑥 =

$𝟏𝟒, 𝟔𝟓𝟎? $𝟐𝟖, 𝟎𝟎𝟎?

introduction to function( general mathematics)

introduction to function( general mathematics)

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