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Practicalities in

GENERAL MATHEMATICS

Let's DO it the

MATH WAY!!!

Welcome to

the World of

About the Subject

GENERAL

MATHEMATICS

GEN MATH

Difficult

Subject???

???

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GEN

MATH

Nerve-wracking???

???

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GEN MATH

Boring

lessons???

???

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GEN MATH

???

Core Subject in Grade 11

piecewise rational exponential logarithmic

solving equations and inequalities

identifying the domain, range, intercepts and asymptotes

GEN MATH

interest annuities

loans

stocks

bonds

propositions

fallacies

arguments

???

Function

Business Math

Logic

Are you now ready to explore

???

GEN MATH?

Objectives

LESSON: FUNCTIONS

Objectives

Illustrate a piecewise function

Describe a function as a model

Illustrate a relation and a function

Represent real-life situations using functions

Match the items on the left with the items in the right that is related to it.

Let's Explore Relations!

Function

and

Relation

RELATION

It is a set of ordered pairs (x, y).

Students

It is a relationship between two sets of values:

set of x-values

set of y-values

R = { (-1,2), (0,2), (1,-3), (2,-2), (8,3) }

Price

Table of Values

Mapping Diagram

R = { (-1,2), (0,2), (1,-3), (2,-2), (8,3) }

Birthday

Mapping Diagram

One-to-one Correspondence

Square of a number

Many-to-one Correspondence

One-to-many Correspondence

One-to-one Correspondence

Many-to-one Correspondence

One-to-many Correspondence

Parents to a child

A. One-to-one

B. Many-to-one

C. One-to-many

A teacher to his/her students

A. One-to-one

B. Many-to-one

C. One-to-many

Refer to the given mapping diagram.

A. One-to-one

B. Many-to-one

C. One-to-many

A student to his/her fingerprint

A. One-to-one

B. Many-to-one

C. One-to-many

Number 25 to its square roots

A. One-to-one

B. Many-to-one

C. One-to-many

R = { (-1,2), (0,2), (1,-3), (2,-2), (8,3) }

Bar code

J = { (-1,4), (0,3), (1,2), (2,1), (3,0) }

Reflect:

What are your relationship goals in life?

How is your relation with your parents?

What about your relation with your friends?

Let's Explore Functions!

A function is a relation.

Integers

How do we know if the given relation is a function?

No two ordered pairs have the same x-values but different y-values

E = { (1, 5), (2, 4), (3, 3), (4, 2) }

E = { (1, 5), (2, 4), (3, 3), (4, 2) }

FUNCTION

C = { (3, -1), (0, 2), (3, -4), (5, 1) }

C = { (3, -1), (0, 2), (3, -4), (5, 1) }

NOT FUNCTION

Mere RELATION

How do we know if the given relation is a function?

One-to-one correspondence

Many-to-one correspondence

= FUNCTION

One-to-many correspondence

= NOT FUNCTION

Many-to-one Correspondence

FUNCTION

One-to-many Correspondence

Mere RELATION

NOT FUNCTION

How do we know if the given relation is a function?

Vertical Line Test

exactly 1 point

FUNCTION

2 or more points

NOT FUNCTION

FUNCTION

Mere RELATION

NOT FUNCTION

Relation

Function

All functions are relations.

All relations are functions.

NF

F

f = {(0, -1), (2, -5), (4, -9), (6, -13)}

f = {(1, 7), (2, -5), (1, 6), (2, -8)}

f = {(0, -1), (2, -5), (4, -9), (6, -13)}

f = {(1, 7), (2, -5), (1, 6), (2, -8)}

one-to-one correspondence

many-to-one correspondence

Function as a Model

Imagine a function as a machine.

Function

as a Model

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Input

Domain of the function

Set of

x-values

Output

Range of the function

Set of

y-values

Function Machine

INPUT:

Collect the dirt

OUTPUT:

Clean floor

Not a function

OUTPUT:

Good

grades

INPUT:

Study

Well

Function Machine:

Student

Function

OUTPUT:

Reactions

INPUT:

Posting on socmed

Function Machine:

Netizen

Reflect:

How do you function as a human-being?

Are you a functional individual?

What are your "inputs" and "outputs" in life?

Function Machine

x = 1

f(x) = x+4

f(x) = 5

Domain:

All Real numbers

Range:

All Real numbers

Function:

F(x) or f(x)

Problem-solving:

Functions in real-life.

Function in Real-Life

Nan and Dino are best of friends. They decided to have an online food business. They bought baking tools and other materials in market and made cookies to sell to their friends. Their starting capital is worth 1000 pesos which can make 100 pieces of palm-sized cookies. If they sell it for 20 pesos each, how much is their profit?

Give a function C that can represent the cost of purchasing a COVID-19 Antibodies rapid testing kit, if one kit costs 1, 500 pesos.

C(x) = 1500x

Function:

P(n) = 20n – 1000

= 20 (100) - 1000

P(n) = 1000

Piecewise

Function

Piecewise Function

It is a function as it sounds like. It is a function made of pieces.

A user is charged 300 pesos monthly for a particular mobile plan, which includes 100 free text messages. Messages in excess of 100 are charged 1 peso each. Represent the amount a consumer pays each month as a function of the number of messages m sent in a month.

Happy Learning

FerNanDino Teens!!!

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