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Practicalities in
Let's DO it the
MATH WAY!!!
Difficult
Subject???
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Nerve-wracking???
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Boring
lessons???
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piecewise rational exponential logarithmic
solving equations and inequalities
identifying the domain, range, intercepts and asymptotes
interest annuities
loans
stocks
bonds
propositions
fallacies
arguments
LESSON: FUNCTIONS
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!
RELATION
It is a set of ordered pairs (x, y).
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) }
Table of Values
Mapping Diagram
R = { (-1,2), (0,2), (1,-3), (2,-2), (8,3) }
Mapping Diagram
R = { (-1,2), (0,2), (1,-3), (2,-2), (8,3) }
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.
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
FUNCTION
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
Imagine a function as a machine.
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Domain of the function
Set of
x-values
Range of the function
Set of
y-values
INPUT:
Collect the dirt
OUTPUT:
Clean floor
Not a function
OUTPUT:
Good
grades
INPUT:
Study
Well
Function
OUTPUT:
Reactions
INPUT:
Posting on socmed
Reflect:
How do you function as a human-being?
Are you a functional individual?
What are your "inputs" and "outputs" in life?
x = 1
f(x) = x+4
f(x) = 5
Domain:
All Real numbers
Range:
All Real numbers
Functions 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
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!!!