General Mathematics
By : DarkRaven
diagram, which consists of a box showing
LESSON 1: FUNCTIONS - (FUNCTIONS AND the input, output, and the rule which is often
OPERATION ON FUNCTIONS) written inside the box. The second way is to
use two sets, one to represent the input and
Definition : one to represent the output with an arrow
showing the relationship between them.
A relation is a set of ordered pairs. The domain of a
relation is the set of first coordinates. The range is the
set of second coordinates Functions in Real Life :
EX: (2,10)
1. Buying Rice in the market and its the price
( The 2 is the domain and 10 is a range ) per quantity
2. Internet Surfing fee and its hourly surfing
A function is a relation in which each element of the rate
domain corresponds to exactly one element of the 3. A person’s salary depends on the number of
range. This is denoted by y = f(x) hours worked
Additional Information
Function Rule
Concept of Function
A function is a set of ordered pairs (x,y) such that no
two ordered pairs have the same x-value but different
y-values. Using functional notation, we can write f(x) =
y, read as “f of x is equal to y”. In particular if (1,2) is
an ordered pair associated with the function f, then we
say f(1)=2
On the other hand, the vertical line test can be used
to identify if the graph is a function. A graph
represents a function if and only if each vertical line
intersects the graph at most once.
𝐹(𝑥) = 3𝑋
Function Rule
F = Name/Label
- A function can be thought of as a rule, which
(x) = Input
operates on an input and produces an
3x = Output ( Value of the Function )
output. This is often illustrated pictorially in
two ways. The first way is by using a block
1
, General Mathematics
By : DarkRaven
IN WORDS : The rule of F is to “ Multiply the input by
Number of Months Ticket Price
3 “ of F of F x is equal to 3 times x.
6 months or more PHP 1,250.00
before the flight date
Piecewise Function
5 months before the PHP 1,550.00
Definition: flight date
- is a function defined by multiple
sub-functions, where each sub-function 3 months before the PHP 1,750.00
flight date
applies to a certain interval of the main
function domain? A month before the PHP 2,250.00
- is a function that has different rules for flight date
different parts of its domain.
Real-Life Applications
- The price of airline tickets 5 months before
the flight is constantly changing until such
time as the flight schedule comes near. EXAMPLE :
- Prices of utilities like water, electricity are Suppose Garry wants to determine the relationship of
different charges per interval. the price of NFA rice per kilo in the market and the
following information is given.
- School offers discounts depending on the
number of siblings enrolling in the same ● One kilo of rice costs PHP 40.00
school. ● He wants to buy 3 kilos of rice.
● He wants to determine the amount of rice he
EXAMPLE: can purchase with PHP 200.00 in his pocket.
A hotel has a special promo for their air-conditioned
Number of Cost (y) Computations
room (good for two people). It charges Php 1,200 for
kilos of Rice
a maximum stay of two nights and Php 300 for an (x)
additional night’s stay. The total cost T is a function of
the number of nights x that a guest stays. 1 PHP 40.00 40 (1) = 40
A.) The piecewise function is: 2 PHP 80.00 40 (2) = 80
B.) T(4) =1,200 +300 (4-2 3 PHP 120.00 40 (3) = 120
= Php 1,800
4 PHP 160.00 40 (4) = 160
5 PHP 200.00 40 (5) = 200
6 PHP 240.00 40 (6) = 240
Mathematically, we have y = 40x. (This indicates that
EXAMPLE 6: Suppose Philippine Airlines offered the the total cost (y) is equal to 40 times the number of
discount on tickets from Davao to Manila utilizing the kilos (x) of rice.
table below:
2
By : DarkRaven
diagram, which consists of a box showing
LESSON 1: FUNCTIONS - (FUNCTIONS AND the input, output, and the rule which is often
OPERATION ON FUNCTIONS) written inside the box. The second way is to
use two sets, one to represent the input and
Definition : one to represent the output with an arrow
showing the relationship between them.
A relation is a set of ordered pairs. The domain of a
relation is the set of first coordinates. The range is the
set of second coordinates Functions in Real Life :
EX: (2,10)
1. Buying Rice in the market and its the price
( The 2 is the domain and 10 is a range ) per quantity
2. Internet Surfing fee and its hourly surfing
A function is a relation in which each element of the rate
domain corresponds to exactly one element of the 3. A person’s salary depends on the number of
range. This is denoted by y = f(x) hours worked
Additional Information
Function Rule
Concept of Function
A function is a set of ordered pairs (x,y) such that no
two ordered pairs have the same x-value but different
y-values. Using functional notation, we can write f(x) =
y, read as “f of x is equal to y”. In particular if (1,2) is
an ordered pair associated with the function f, then we
say f(1)=2
On the other hand, the vertical line test can be used
to identify if the graph is a function. A graph
represents a function if and only if each vertical line
intersects the graph at most once.
𝐹(𝑥) = 3𝑋
Function Rule
F = Name/Label
- A function can be thought of as a rule, which
(x) = Input
operates on an input and produces an
3x = Output ( Value of the Function )
output. This is often illustrated pictorially in
two ways. The first way is by using a block
1
, General Mathematics
By : DarkRaven
IN WORDS : The rule of F is to “ Multiply the input by
Number of Months Ticket Price
3 “ of F of F x is equal to 3 times x.
6 months or more PHP 1,250.00
before the flight date
Piecewise Function
5 months before the PHP 1,550.00
Definition: flight date
- is a function defined by multiple
sub-functions, where each sub-function 3 months before the PHP 1,750.00
flight date
applies to a certain interval of the main
function domain? A month before the PHP 2,250.00
- is a function that has different rules for flight date
different parts of its domain.
Real-Life Applications
- The price of airline tickets 5 months before
the flight is constantly changing until such
time as the flight schedule comes near. EXAMPLE :
- Prices of utilities like water, electricity are Suppose Garry wants to determine the relationship of
different charges per interval. the price of NFA rice per kilo in the market and the
following information is given.
- School offers discounts depending on the
number of siblings enrolling in the same ● One kilo of rice costs PHP 40.00
school. ● He wants to buy 3 kilos of rice.
● He wants to determine the amount of rice he
EXAMPLE: can purchase with PHP 200.00 in his pocket.
A hotel has a special promo for their air-conditioned
Number of Cost (y) Computations
room (good for two people). It charges Php 1,200 for
kilos of Rice
a maximum stay of two nights and Php 300 for an (x)
additional night’s stay. The total cost T is a function of
the number of nights x that a guest stays. 1 PHP 40.00 40 (1) = 40
A.) The piecewise function is: 2 PHP 80.00 40 (2) = 80
B.) T(4) =1,200 +300 (4-2 3 PHP 120.00 40 (3) = 120
= Php 1,800
4 PHP 160.00 40 (4) = 160
5 PHP 200.00 40 (5) = 200
6 PHP 240.00 40 (6) = 240
Mathematically, we have y = 40x. (This indicates that
EXAMPLE 6: Suppose Philippine Airlines offered the the total cost (y) is equal to 40 times the number of
discount on tickets from Davao to Manila utilizing the kilos (x) of rice.
table below:
2
