This document provides 11 examples of real-life situations and asks the student to represent each as a mathematical function model. The situations include examples related to salaries, business expenses, medical dosages, event fees, and more. The student is expected to be able to analyze each situation and write the appropriate function that could model the relationship between variables in each case.

1. General Mathematics
Quarter 1 – Module 1:
Functions as Models

2. General Mathematics – Grade 11
Alternative Delivery Mode
Quarter 1 – Module 1: Functions as Models
First Edition, 2020
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Office Address: Provincial Capitol Compound, Balanga City, Bataan
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3. General Mathematics
Quarter 1 – Module 1:
Functions as Models

4. 1
Introductory Message
For the facilitator:
Welcome to the General Mathematics – Grade 11 Alternative Delivery Mode (ADM)
Module on Functions as Models!
This module was collaboratively designed, developed, and reviewed by
educators both from public and private institutions to assist you, the teacher or
facilitator in helping the learners meet the standards set by the K to 12 Curriculum
while overcoming their personal, social, and economic constraints in schooling.
This learning resource hopes to engage the learners into guided and
independent learning activities at their own pace and time. Furthermore, this also
aims to help learners acquire the needed 21st century skills while taking into
consideration their needs and circumstances.
In addition to the material in the main text, you will also see this box in the
body of the module:
As a facilitator you are expected to orient the learners on how to use this
module. You also need to keep track of the learners' progress while allowing them to
manage their own learning. Furthermore, you are expected to encourage and assist
the learners as they do the tasks included in the module.
Notes to the Teacher
This contains helpful tips or strategies that
will help you in guiding the learners.

5. 2
For the learner:
Welcome to the General Mathematics – Grade 11 Alternative Delivery Mode
(ADM) Module on Functions as models!
We often describe a phenomenon mathematically, to help us better
understand our world, and using Functions is one way to do it. Functions may have
their limitations but a precise model using one can provide valuable results and
conclusions.
This module was designed to provide you with fun and meaningful
opportunities for guided and independent learning at your own pace and time. You
will be enabled to process the contents of the learning resource while being an active
learner.
This module has the following parts and corresponding icons:
What I Need to Know This will give you an idea of the skills or
competencies you are expected to learn in the
module.
What I Know This part includes an activity that aims to
check what you already know about the
lesson to take. If you get all the answers
correct (100%), you may decide to skip this
module.
What’s In This is a brief drill or review to help you link
the current lesson with the previous one.
What’s New In this portion, the new lesson will be
introduced to you in various ways such as a
story, a song, a poem, a problem opener, an
activity or a situation.
What is It This section provides a brief discussion of the
lesson. This aims to help you discover and
understand new concepts and skills.
What’s More This comprises activities for independent
practice to solidify your understanding and
skills of the topic. You may check the
answers to the exercises using the Answer
Key at the end of the module.
What I Have Learned This includes questions or blank
sentence/paragraph to be filled in to process
what you learned from the lesson.
What I Can Do This section provides an activity which will
help you transfer your new knowledge or skill
into real life situations or concerns.

6. 3
Assessment This is a task which aims to evaluate your
level of mastery in achieving the learning
competency.
Additional Activities In this portion, another activity will be given
to you to enrich your knowledge or skill of the
lesson learned. This also tends retention of
learned concepts.
Answer Key This contains answers to all activities in the
module.
At the end of this module you will also find:
The following are some reminders in using this module:
1. Use the module with care. Do not put unnecessary mark/s on any part of the
module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instructions carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not
hesitate to consult your teacher or facilitator. Always bear in mind that you are
not alone.
We hope that through this material, you will experience meaningful learning and
gain deep understanding of the relevant competencies. You can do it!
References This is a list of all sources used in developing
this module.

7. 4
What I Need to Know
At the end of the lesson, the students are expected to represent real-life
situations using functions, including piece-wise functions M11GM-Ia-1.
Specifically, the students are expected be able to:
 demonstrate how function is being used in daily life; and
 create a model interpreting a piece wise function.

8. 5
What I Know
Represent the following Real-life situation into Function Model.
A. Represent each presented real-life situation as a function model.
1. Jill needs an allowance for her college expenditures. She managed to get a
part-time job that earns Php 75.00 per hour. Help her device a function
model in computing her total salary after a month of work.
2. Aling Kesing delivers meals that cost 45 pesos to her customers daily. If
she delivers 𝑥 number of meals in a day, represent her total earnings as
𝐸(𝑥).
3. One night, Luisa woke-up discovering that her child has fever. She rushed
to the medicinal cabinet and took the medicine. To make sure of the dosage
her child needed, she read the dosage instruction written on the box that
states, “For every 1kg of body mass, a patient must drink 3mL.” What
formula will she use to identify the right dosage for her child?
4. Mt. Tarak is one of the famous hiking sites in Bataan. Every summer,
hikers from different provinces travel to visit the mountain to see the
summit. The local government then passed a resolution that requires
hikers to have local guides to avoid accidents. Hiring a guide will cost a
group Php 300.00 plus environmental fee of Php 50.00 for each member
of the group. How much will each group of different cluster size be billed?
5. Julia wants to sell fried chicken nuggets via moving cart in the market.
She noticed that she will spend Php 15.00 for each nugget and Php 150.00
for cart rent. If 𝐶(𝑥) represents the function for her business’ daily
expenses, how will you represent her situation in a function model?
6. If 𝐶(𝑥) represents a food stall’s daily expenses of 200 pesos for rent space
and a capital of 30 pesos for each siomai meal, what function model will
represent the situation?
7. With the recent social problems brought by the pandemic, most people now
prefer to purchase necessities online. Georgia saw this as an opportunity
to put up an online agri-vet business. Upon finding a supplier that offers
a good deal in agri-vet supplies, she decided to repack the packages into a
more affordable 1kg packs. She adds 50 pesos for every 1-kg pack of pet
food that originally costs 195 pesos. Consider 𝑐(𝑥) as the total amount sold
for a week to create an appropriate function model.

9. 6
8. A car for hire can be rented for 3000 pesos with an additional daily rate of
1500 pesos. Represent the total rental fee 𝑅(𝑥) in an 𝑥 number of days.
9. Represent the daily total earnings 𝑇(𝑥) of an online video site considering
the 𝑥 number of views that costs 5 pesos per view.
10. A writer can write a novel at a rate of 3 pages per 5-hour work. If he wants
to finish the novel in 𝑥 number of pages, determine a function model that
will represent the accumulated writing hours to finish his novel.
11. Determine the function model that represents the number of hours until a
certain mobile phone battery goes from full charged to empty if it only
needs an hour to be at 90%.
12. The courier company charges Php 30.00 per package weighing 3 kilos or
less, and an additional of Php 4.00 per kilo if the package exceeds 3 kilos.
The courier also told Georgia that they cannot ship items more than
15kilos.
13. Bataan Money Express is a money transfer company that charges 25 pesos
for an amount less than Php 500.00, 45 pesos for an amount more than
or equal to Php 500.00, 65 pesos for an amount more than or equal to Php
750.00 and 85 pesos beyond Php 1000.00.
14. Knowing that most Filipinos love to sing, Bianca invested in videoke
business. She came up with the following scheme: Php 750.00 for 2 days
rent and an additional of Php 250.00 for each exceeding day.
15. Every weekend, Marisol, a Senior High School student specializing in
Bread and Pastries, helps in her aunt’s siopao business to earn extra
allowance. She receives Php 1.00 each for the first 25 packs of siopao she
finishes packing; Php 1.25 each for the next 25 packs and Php 1.50 each
in excess of 50 packs. Consider 𝑆(𝑥) as the total amount of commission for
a weekend of packing siopao in representing the situation as a function
model.

10. 7
Lesson
1 Functions as models
Function is a mathematical relation within two objects: an input and output, and
that the output is related to the input by some rule.
Function can be seen in real life situations and is very useful in almost all walks of
life, as it interpret these scenarios in mathematical models.
What’s In
Let us have a short review on Function by getting over again with the basic concept
and representation of function.
 A function 𝒇 from set A (input) to set B (output) is
a rule of correspondence that assigns to each
element x in the set A exactly one element y in the
set B; or
 Each x can have only one y, but it CAN be the
same y as another x gets assigned to.
In other words:
a. all x’s (inputs) are assigned;
b. No x (input) has more than one y (outputs) assigned
F U N C T I O N

11. 8
Set A (x)
inputs
1 2 3 4 5 6
Set B (y)
outputs
2 3 4 5 6 7
Set A input (x)
Domain
1
2
3
4
5
Set B output (y)
Range
1
5
4
3
2
6
𝒇(𝒙) = 𝒙 + 𝟏
𝑖𝑛𝑝𝑢𝑡 3 𝑜𝑢𝑡𝑝𝑢𝑡 4
𝒇(𝟑) = 𝟑 + 𝟏 = 𝟒
𝒇(𝒙) = 𝒙 + 𝟏
𝑖𝑛𝑝𝑢𝑡 𝑎 𝑜𝑢𝑡𝑝𝑢𝑡 (𝑎) + 1
𝒇(𝒂) = 𝒂 + 𝟏

12. 9
Identify if each set of objects is a FUNCTION or NOT. The variable x represents
the input, and the variable y represents the output.
1. 𝑥 = 𝑎𝑢𝑡𝑜𝑚𝑜𝑏𝑖𝑙𝑒
𝑦 = 𝑝𝑙𝑎𝑡𝑒 𝑛𝑢𝑚𝑏𝑒𝑟
2. 𝑥 = 𝑚𝑎𝑡ℎ 𝑡𝑒𝑎𝑐ℎ𝑒𝑟
𝑦 = 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑖𝑛 𝑎 𝑐𝑙𝑎𝑠𝑠
3. 𝑥 = 𝑍𝐼𝑃 𝑐𝑜𝑑𝑒
𝑦 = 𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑜𝑤𝑛
4. 𝑥 = 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
𝑦 = 𝑍𝐼𝑃 𝑐𝑜𝑑𝑒
5. 𝑥 = 𝑠ℎ𝑜𝑒 𝑠𝑖𝑧𝑒
𝑦 = 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝑎 𝑐𝑙𝑎𝑠𝑠
6. 𝑥 = 𝑙𝑜𝑐𝑘𝑒𝑟 𝑛𝑢𝑚𝑏𝑒𝑟
𝑦 = 𝑠𝑡𝑢𝑑𝑒𝑛𝑡
7. 𝑥 = 𝑐𝑜𝑠𝑡
𝑦 = 𝑝𝑟𝑜𝑑𝑢𝑐𝑡
8. 𝑥 = 𝑓𝑎𝑚𝑖𝑙𝑦 𝑚𝑒𝑚𝑏𝑒𝑟
𝑦 = 𝑠𝑜𝑐𝑖𝑎𝑙 𝑠𝑒𝑐𝑢𝑟𝑖𝑡𝑦 𝑛𝑢𝑚𝑏𝑒𝑟
9. 𝑥 = 𝑠𝑡𝑟𝑒𝑒𝑡 𝑎𝑑𝑑𝑟𝑒𝑠𝑠
𝑦 = 𝑓𝑎𝑚𝑖𝑙𝑦 𝑚𝑒𝑚𝑏𝑒𝑟𝑠
10. 𝑥 = ℎ𝑒𝑖𝑔ℎ𝑡
𝑦 = 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑖𝑛 𝑎 𝑐𝑙𝑎𝑠𝑠

13. 10
What’s New
Consider the scenario below and try to relate it to the concept of function.
Scenario A.
Gas 11-A students list down their grades in
General Mathematics. Basically, each
student has only one grade for Gen Math but
more than one student can get the same
grade.
Scenario B.
In our canteen, all kinds of juices are worth
Php 5.00 each cup. There is mango juice,
pineapple juice, guava juice, chocolate juice,
buko juice, and many more to choose from.
Ana wants to buy 2 different juices, while
Brenda wants to buy 3 different juices.
Set A
Name of Students
input (x)
Domain
Set B List of Gen
Math Grades
output (y)
Range
Arnold
92
Beth
Chip
Deam
Erriz
91
90
93
89
Set A
Juice Flavors
input (x)
Domain
Set B List of Gen
Price per cup output
(y)
Range
2
3
Php 5.00
Php 10.00
Php 15.00
Php 20.00
1

14. 11
Scenario C.
A grade 11 student who decided to ride a
tricycle going home from school, noticed a
table of fares posted inside the vehicle. He
read the fare guide during the trip and found
out that he needed to pay 10 pesos as the
basic fare that covers a 5-kilometer ride and
an additional 1 peso every exceeding
kilometer.
Set A
Distance in Km
input (x)
Domain
Set B List of Gen
Tricycle Fare
output (y)
Range
3 km
Php 11.00
5 km
6 km
7 km
8 km
Php 12.00
Php 13.00
Php 10.00
Php 14.00

15. 12
From the above real-life situation, answer the following questions for scenario A.
A.1. Is it logical that each student gets only one grade? Can we consider this an
example of a function?
A.2. Is It also logical that more than one (say 3 students) can get the same grades
as the others? Is this scenario a function?
A.3. Is it possible that one of your classmate does not have a grade in Gen Math?
Is this an example of a function??
A.4. Which of the following will represent the function scenario into function
model as 𝑥 be the name of each students and 𝑦 be the grades of
students?
(a) 𝑦 = 𝑥 (b) 𝑦 = 2𝑥 (c) 𝑦 = 𝑥 (d) 𝑦 = 𝑥 + 2
What is It

16. 11
Consider real-life Scenario B and try to answer the following questions:
B.1.Can we consider the relation of the total price of what Ana and Brenda will
pay to the number of juices they are going to buy a function?
B.2. Will the total amount of payment be your input (𝑥)? or output (𝑦)?
B.3.Will the number of juices they wanted to buy be your input (𝑥)?
or output (𝑦)?
B.4.How will you represent it as a function model?
Bear in mind that 𝑦 𝑐𝑎𝑛 𝑏𝑒 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 𝑎𝑠 𝑓(𝑥)
(a) 𝑓(𝑥) = 𝑥 + 5 (b) 𝑓(𝑥) = 5𝑥 (c) 𝑓(𝑥) = 𝑥
(d) 𝑓(𝑥) =
Consider real-life Scenario C and try to answer the following questions:
C.1.What did you notice? Did you find the scenario different from the two
previous situations?
C.2.What seems different?
C.3.Can we still consider the situation a function?
C.4.Will you write a simple mathematical model to understand it more?
Consider: 𝑘 as the total kilometer ride and 𝑇(𝑘) as the total fare.
Function is often used in interpreting scenarios in life into mathematical models
mostly called Function Models. These function models lead us to a better
understanding of various occurrences.
In a Piecewise Function, the input is divided into pieces of a formula with each piece
having their own condition or rule to deduce the output. It shows a set of different
intervals that behaves differently.
In your early stage of learning Math, you have already encountered this piecewise
function, that is the Absolute Value defined as:
𝒇(𝒙) =
−𝒙, 𝒙 < 𝟎
𝒙, 𝒙 ≥ 𝟎

17. 12
A. Use the guide questions below in representing each real-life scenario as a
function model.
a. Which represents as the input 𝑥?
b. Which represents as the output 𝑓(𝑥)?
c. How will you represent the scenario into a function model?
1. Mr. Anniz noticed that his motorcycle consumes 1 liter of
gasoline from his home going to Vista Mall which is 15
kilometers apart.
2. Romer transferred a three - leaf tomato
tree from a pot to the soil. The next
morning, Romer was surprised to see
three new leaves have sprouted. The
following day, he expected the tree to
have 9 leaves, and he was right.
3. In this time of pandemic, some businesses took action to adapt
to the new normal. Boyet, a computer shop owner, came up with
an ingenious solution which he called, “Rent a Comp”. The
concept is to lend a computer, which is packed with a device that
computes or counts the time of usage, to a costumer. The renter
needs to pay an initial of Php 600.00 for a total of 500 hours,
and an additional amount of 2 pesos for the excess time per
hour.
What’s More

18. 13
What I Have Learned
What are the things you need to consider to create a function model from a real-life
scenario? And on piecewise function model? Use the table below to answer the given
questions.
FUNCTION MODEL PIECEWISE FUNCTION

19. 14
What I Can Do
Write a situation or scenario that happened to you like buying on a store or riding a
bike that you can relate with our topic “Function as a Model". Try to give a detailed
story that will be easy to understand. In addition to that, create a Function Model
for your scenario.

20. 15
Assessment
B. Represent each presented real-life situation as a function model.
1. Along the street of Townsite proper, a canteen rose to popularity. They offer
a meal that costs 30 pesos with free soup. This is the reason why most of
the companies and small business staffs around the area continue to order
in bulk.
2. Judas, a welder in a large machine company, earns Php 600.00 a day for
an 8-hour work. His wife devised a function model to solve how much will
his monthly salary be depending on the number of days he worked for the
company.
3. A mobile company devised a plan to eliminate the burden of paying a large
amount of money for their cellphone unit. The plan offers buyers the option
of monthly payments for a specific period of time. Ruina read the poster
and availed the unit. The contract states that she will pay 200 pesos
monthly and an additional hourly charge of 5 pesos for the data usage in
a span of 3 years. Consider 𝐶(𝑥) as the monthly payment of Ruina.
4. Lauro, an OFW arrived at the Philippines in the middle of the pandemic.
The only way to reach his home is to grab a taxi that costs ten times the
distance travelled. How will you represent the fare, 𝐶(𝑥), as a function
model considering the distance (𝑥) they have travelled?
5. Lobrada Family got a tour package to spend their summer vacation in
northern part of Luzon. They rented a van for Php 5 000.00 plus an
additional daily rate of Php 900.00. Device a function model that will help
them identify the total cost of their rented van.
6. Due to the pandemic, some private schools were forced to shut down.
Thus, private teachers are left with no work. Solomon is one of the teachers
who lost their job. He decided to put up a tutoring service for Senior High
School Math students and charged one of his tutees Php 150.00 for 2
hours and the other Php 450.00 for 6 hours of tutoring. Device a function
model Solomon used to figure out how much will his tutees be billed for a
certain number of hours of tutorial.

21. 16
7. Merac, a game developer created a mobile game. He doesn’t want his game
to be sold to a game development company, thinking that he will lose his
name as the original developer. Instead, he uploaded it in the Google play
store and charged 250 pesos for access to the game. He wants to determine
a function model that will determine his proceeds with respect to the
number of persons who downloads the game.
8. Adam can paint a 40 square meter wall in 3 hours. If he can paint the
whole house in just 𝑥 hours, what function model will help him determine
the total area of the walls he painted?
9. Miranda bought a brand-new cell phone. She noticed that the battery
consumes a rate of 5% per half an hour. Determine a function model that
represents the amount of battery left after a period of time.
10. Georgia started an online business selling baking supplies because of the
very high demand brought by lockdowns due to the pandemic. Most people
cannot go out to purchase their baking necessities so she thought this is
a great opportunity to earn. In doing so, she needs to know how much the
shipping fee costs, then breakdown her expenses and proceeds. She
immediately communicated with the nearest courier company in their
community and learned that it can cost her Php 50.00 per packages
weighing 2 kilos or less, and an additional Php 5.00 every kilo for a package
that weighs more than 2 kilos. The courier also told Georgia that they
cannot ship items more than 10kilos.
11. In a certain private resort, the manager devised a plan to help market the
venue. The plan is to offer a discount depending on the size of the group.
An entrance fee of Php 150.00 per head for a group of 20 persons or less,
Php 145.00 per head for a group of 21 to 50 persons, and Php 130.00 per
head for a group of 51 to 100 persons. If the group exceeds 100, the resort
will charge them Php 100.00 each person only.
12. Marco and Marca are planning to get married this coming June. To have
an idea of a better catering service plan, they consulted their wedding
organizer. One catering service offers Php 200.00 per plate for 50 persons;
Php 175.00 per plate for more than 50 persons up to 150; Php 150.00 per
plate for more than 150 up to 250; and Php 120 per plate for more than
250.

22. 17
13. A money transfer company charges 50 pesos for an amount less than
Php 1000.00, 75 pesos for an amount more than or equal to Php 1000.00,
and 100 pesos beyond Php 2000.00.
14. Paul is planning to hold his 40th birthday party in a private resort for at
least 2 days. Knowing that his friends love to sing, he rented a videoke
machine for Php 800.00, and an additional of Php 300.00 for each day of
extension.
15. Boyong, a Senior High school student earns his allowance, via commission,
by helping his mother every weekend in their small business of selling
tapa. He receives a commission of 1 peso every kilo for the first 10 kilos of
smoked fish, 2 pesos every kilo for the next ten kilos, and 4 pesos each kilo
in excess of 20kilos. Consider 𝑆(𝑥) as the total amount of commission for
a weekend of selling Smoked Fish.

23. 18
Additional Activities
Devise a logical and appropriate series of mathematical statements to better
understand representing real-life situations stated below into function model.
Use the hints provided after each problem.
1. At an early age, Amber invested on
farmlands and started building his
farm during his days off. Today, he
bought a 200m fence-wire to construct
an enclosure for his cows to protect his
planted veggies. Consider the function
𝐴(𝑥) as the area that can enclosed
using the bought fence-wire with
respect to its length (𝑥). Hint: Recall the
concepts and formulas of area and
perimeter of rectangle.
2. A 300 - meter fencing material is to be
used to enclose a rectangular property. An
existing property fence will be utilized on
one side of the pen. If x represents its area
in terms of A(x). Hint: Recall the concepts
and formula in area and perimeter of a
rectangle

24. 19
3. Using a 16 square inch sheet of
rectangular piece of tin, a cylindrical
pipe will be molded. Determine a
function model for the largest volume
of cannister that can be molded out of
it. Hint: Recall the concepts and
formulas of the volume of a cylinder.
4. Armin wants to know how a certain tarpaulin printing shop bills their
customers. He gathered all the data he could get from some of the previous
customers and create it in a table. Help Armin device a formula used by
the tarp printing shop using the data below. Hint: Recall the formulas of
slope of linear equations.
Tarp in sq. in (x) 1 4 9 16 25
Amount billed (y) 13 22 37 58 85

25. 20
Answer Key
What
I
Know:
1.
𝒇(𝒙)
=
𝟕𝟓𝒙
2.
𝑬(𝒙)
=
𝟒𝟓𝒙
3.
𝒇(𝒙)
=
𝟑𝒙
4.
𝒇(𝒙)
=
𝟓𝟎𝒙
+
𝟑𝟎𝟎
5.
𝑪(𝒙)
=
𝟏𝟓𝒙
+
𝟏𝟓𝟎
6.
𝑪(𝒙)
=
𝟑𝟎𝒙
+
𝟐𝟎𝟎
7.
𝑪(𝒙)
=
(𝟏𝟗𝟓
+
𝟓𝟎)𝒙
8.
𝒇(𝒙)
=
𝟑𝟎𝟎𝟎
+
𝟏𝟓𝟎𝟎𝒙
9.
𝑻(𝒙)
=
𝟓𝒙
10.
𝒇(𝒙)
=
𝟓
𝟑
𝒙
11.
𝒇(𝒙)
=
𝟏𝟎𝟎
−
𝟏𝟎𝒙
12.
𝒇(𝒙)
=
𝟑𝟎
𝟑𝟎
+
𝟒(𝒙
−
𝟑)
;𝒊𝒇
𝟎
𝒙
𝟑
;𝒊𝒇
𝟑
𝒙
𝟏𝟓
13.
𝒇(𝒙)
=
𝟐𝟓;
𝟒𝟓;
𝟔𝟓
𝟖𝟓
;𝒊𝒇
𝟎
𝒙
𝟓𝟎𝟎
;𝒊𝒇
𝟓𝟎𝟎
𝒙
𝟕𝟓𝟎
;𝒊𝒇
𝟕𝟓𝟎
𝒙
𝟏𝟎𝟎𝟎
:
𝒊𝒇
𝒙
𝟏𝟎𝟎𝟎
14.
𝒇(𝒙)
=
𝟕𝟓𝟎
𝟕𝟓𝟎
+
𝟐𝟓𝟎(𝒙
−
𝟐)
;𝒊𝒇
𝟎
𝒙
𝟐
;𝒊𝒇
𝒙
𝟐
15.
𝑺(𝒙)
=
𝒙;
𝒊𝒇
𝟎
<
𝒙
≤
𝟐𝟓
𝟏.
𝟐𝟓(𝒙
−
𝟐𝟓)
+
𝟐𝟓;
𝒊𝒇
𝟐𝟓
<
𝒙
≤
𝟓𝟎
𝟏.
𝟓𝟎(𝒙
−
𝟓𝟎)
+
𝟓𝟔.
𝟐𝟓;
𝒊𝒇
𝒙
>
𝟓𝟎
What’s
In:
1.Function
2.Not
Function
3.Function
4.Function
5.Not
Function
6.Function
7.Not
Function
8.Function
9.Not
Function
10.
Not
Function
What
is
It:
A.1.Yes,
a
function
A.2.Yes,
a
function
A.3.No,
not
function
A.4.(a)
𝑦
=
𝑥
B.1.Yes
B.2.Output
B.3.Input
B.4.(𝑏)𝑓(𝑥)
=
5𝑥
C.1.There
are
more
than
one
conditions,
yes
C.2.The
possible
input
is
divided
into
pieces
C.3.Yes,
it
is
called
Piecewise
Function
C.4.𝑇(𝑘)
=
10;
𝑖𝑓
0
<
𝑘
≤
5
10
+
(𝑘
−
5);
𝑖𝑓
𝑘
>
5

26. 21
What
I
Can
Do:
The
student’s
answer
may
vary.
What’s
More:
1.a.
𝑥
as
the
liter
of
gasoline
1.b.
𝑓(𝑥)
as
the
distance
travelled
1.c.
𝑓(𝑥)
=
15𝑥
2.a.
𝑥
as
the
number
of
days
2.b.
𝑓(𝑥)
as
the
number
of
leaves
2.c.
𝑓(𝑥)
=
3𝑥
3.a.
𝑥
as
the
number
of
hours
consumed
3.b.
𝑓(𝑥)
as
the
total
amount
3.c.
𝑓(𝑥)
=
600
;
600
+
2(𝑥
−
500)
;
Assessment:
1.
𝑓(𝑥)
=
30𝑥
2.
𝑓(𝑥)
=
600𝑥
3.
𝐶(𝑥)
=
200
+
5𝑥
4.
𝐶(𝑥)
=
10𝑥
5.
𝑓(𝑥)
=
5000
+
900𝑥
6.
𝑓(𝑥)
=
75𝑥
7.
𝑓(𝑥)
=
250𝑥
8.
𝑓(𝑥)
=
𝑥
9.
𝑓(𝑥)
=
100
−
10𝑥
10.
𝑓(𝑥)
=
50
;
𝑖𝑓
0
<
𝑥
≤
2
50
+
5(𝑥
−
2);
𝑖𝑓
2
<
𝑥
≤
10
11.
𝑓(𝑥)
=
150𝑥;
𝑖𝑓
0
<
𝑥
≤
20
145𝑥;
𝑖𝑓
20
<
𝑥
≤
50
;
;
12.
𝑓(𝑥)
=
;
;
;
;
13.
𝑓(𝑥)
=
;
;
;
:
14.
𝑓(𝑥)
=
800
;
𝑖𝑓
0
<
𝑥
≤
1
800
+
300(𝑥
−
1);
𝑖𝑓
𝑥
>
1
15.
𝑆(𝑥)
=
𝑥;
𝑖𝑓
0
<
𝑥
≤
10
2(𝑥
−
10)
+
10;
𝑖𝑓
10
<
𝑥
≤
20
4(𝑥
−
20)
+
30;
𝑖𝑓
𝑥
>
20
Additional
Activities:
1.
𝐴(𝑥)
=
100𝑥
−
𝑥
2.
𝐴(𝑥)
=
300𝑥
−
2𝑥
3.
𝑉(𝑟)
=
8𝑟
4.
𝑓(𝑥)
=
3𝑥
+
10

27. 22
References
Commission on Higher Education. Teaching Guide for Senior High School General
Mathematics. Diliman, Quezon City. 2016.
Department of Education. General Mathematics Learner’s Manual. Pasig City. 2016.
Department of Education. K to 12 Most Essential Learning Competencies with
Corresponding CG Codes. Pasig City. 2020.
Fernando B. Orines. Next Century Mathematics General Mathematics. Quezon City.
Phoenix Publishing House. 2016.
Margaret L. Lial and Charles D. Miller. Mathematics: with application in the
Management, Natural and Social Studies.Illinios. Scott, Foresman and
Company. 1974.
Max A. Sobel and Norbert Lerner. Algebra and Trigonometry: a pre-calculus Approach.
New Jersey. Prentice-Hall, Inc. 1983.
Raymond A Barnett and Michael R, Ziegler. Precalculus Functions and graphs. New
York. McGraw Hill, Inc. 1993.
Catalina Dinio Mijares.2004. College Algebra Revised Edition. Mandaluyong City.
National Book Store. 2004.

28. For inquiries or feedback, please write or call:
Department of Education – Region III,
Schools Division of Bataan - Curriculum Implementation Division
Learning Resources Management and Development Section (LRMDS)
Provincial Capitol Compound, Balanga City, Bataan
Telefax: (047) 237-2102
Email Address: bataan@deped.gov.ph