Lesson 1 Functions, Function Notations, and Equations.pdf
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Sep 29, 2025
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About This Presentation
GEN MATH
Slide Content
Unit 1: Introduction to Functions • Grade 11
1
Lesson 1
Functions, Function Notations, and
Equations
Table of Contents
Learning Competency 2
Learning Objectives 2
Suggested Time Frame 2
Essential Questions 3
Prerequisite Skills and Topics 3
Lesson Proper 4
- A. Introduction 4
- B. Discussion 6
- C. Practice and Feedback 9
Performance Assessment 13
Synthesis 22
Bibliography 22
1
Lesson 1
Functions, Function Notations, and
Equations
Table of Contents
Learning Competency 2
Learning Objectives 2
Suggested Time Frame 2
Essential Questions 3
Prerequisite Skills and Topics 3
Lesson Proper 4
- A. Introduction 4
- B. Discussion 6
- C. Practice and Feedback 9
Performance Assessment 13
Synthesis 22
Bibliography 22
Unit 1: Introduction to Functions • Grade 11
2
Unit 1 | Introduction to Functions
Lesson 1: Functions, Function Notations, and
Equations
Learning Competency
The learner represents real-life situations using functions, including piece-wise functions
[M11GM-Ia-1].
Learning Objectives
At the end of this lesson, the learner should be able to
• correctly define a function;
• properly represent a function using function notation;
• properly model real-life problems using equations.
Suggested Time Frame
30 minutes
1
1
Suggested time frame is based on the DepEd calendar for A.Y. 2018-2019 and the curriculum guide for mathematics (August
2016 version).
2
Unit 1 | Introduction to Functions
Lesson 1: Functions, Function Notations, and
Equations
Learning Competency
The learner represents real-life situations using functions, including piece-wise functions
[M11GM-Ia-1].
Learning Objectives
At the end of this lesson, the learner should be able to
• correctly define a function;
• properly represent a function using function notation;
• properly model real-life problems using equations.
Suggested Time Frame
30 minutes
1
1
Suggested time frame is based on the DepEd calendar for A.Y. 2018-2019 and the curriculum guide for mathematics (August
2016 version).
Unit 1: Introduction to Functions • Grade 11
3
Essential Questions
At the end of this lesson, the learner should be able to answer the following questions:
• What is a function?
• How will you represent functions?
• How will you determine whether a given equation is a function?
Prerequisite Skills and Topics
Skills:
• Evaluating algebraic expressions
• Illustrating a function
Topics:
• Math 7 Unit 6: Algebraic Expressions | Lesson 2: Evaluating algebraic expressions
• Math 8 Unit 6: Relations and Functions | Lesson 2: Functions
• Math 8 Unit 7: Linear Function | Lesson 1: Equations That Are Linear Functions
• Math 9 Unit 3: Quadratic Functions | Lesson 2: Representing Quadratic Functions
• Math 9 Unit 3: Quadratic Functions | Lesson 5: Determining the Equation of a
Quadratic Function
• Math 10 Unit 9: Polynomial Functions | Lesson 1: Introduction to Polynomial
Functions
Teacher’s Notes
To help better gauge students’ readiness for this lesson, you may assign the short test
given in Test Your Prerequisite Skills section of the corresponding study guide.
3
Essential Questions
At the end of this lesson, the learner should be able to answer the following questions:
• What is a function?
• How will you represent functions?
• How will you determine whether a given equation is a function?
Prerequisite Skills and Topics
Skills:
• Evaluating algebraic expressions
• Illustrating a function
Topics:
• Math 7 Unit 6: Algebraic Expressions | Lesson 2: Evaluating algebraic expressions
• Math 8 Unit 6: Relations and Functions | Lesson 2: Functions
• Math 8 Unit 7: Linear Function | Lesson 1: Equations That Are Linear Functions
• Math 9 Unit 3: Quadratic Functions | Lesson 2: Representing Quadratic Functions
• Math 9 Unit 3: Quadratic Functions | Lesson 5: Determining the Equation of a
Quadratic Function
• Math 10 Unit 9: Polynomial Functions | Lesson 1: Introduction to Polynomial
Functions
Teacher’s Notes
To help better gauge students’ readiness for this lesson, you may assign the short test
given in Test Your Prerequisite Skills section of the corresponding study guide.
Unit 1: Introduction to Functions • Grade 11
4
Lesson Proper
A. Introduction
Suggested Warm-up Activities
Choose from any of the following warm-up activities. These warm-up activities should
either stimulate recall of previous lesson or introduce the lesson and not already used
in the study guide.
Activity 1:
Birth Month Trick
This activity will introduce to
the students the concept of
many-to-one function by
challenging the students to
come up with a reason why
an outcome will always be
the same regardless of their
birth months.
Duration: 10 minutes
Materials Needed: notebook, pen
Methodology:
Ask the students to do the following steps:
1. Take the number of your birth month. (e.g.,
January = 1, February = 2, etc.)
2. Add 32.
3. Add the result in step 2 to the difference between
12 and the number of your birth month.
4. Divide by 2.
5. Subtract 10.
Expected Results:
1. Suppose the student’s birth month is June. June is
represented by 6.
2. Adding 32 to 6 gives 38.
3. Adding the difference of 12 and 6, which is 6, to 38
gives 44.
4. Dividing 44 by 2 gives 22.
5. Subtracting 10 from 22 gives 12.
4
Lesson Proper
A. Introduction
Suggested Warm-up Activities
Choose from any of the following warm-up activities. These warm-up activities should
either stimulate recall of previous lesson or introduce the lesson and not already used
in the study guide.
Activity 1:
Birth Month Trick
This activity will introduce to
the students the concept of
many-to-one function by
challenging the students to
come up with a reason why
an outcome will always be
the same regardless of their
birth months.
Duration: 10 minutes
Materials Needed: notebook, pen
Methodology:
Ask the students to do the following steps:
1. Take the number of your birth month. (e.g.,
January = 1, February = 2, etc.)
2. Add 32.
3. Add the result in step 2 to the difference between
12 and the number of your birth month.
4. Divide by 2.
5. Subtract 10.
Expected Results:
1. Suppose the student’s birth month is June. June is
represented by 6.
2. Adding 32 to 6 gives 38.
3. Adding the difference of 12 and 6, which is 6, to 38
gives 44.
4. Dividing 44 by 2 gives 22.
5. Subtracting 10 from 22 gives 12.
Unit 1: Introduction to Functions • Grade 11
5
Guide Questions:
1. When is your birthday?
2. What number represents that month?
3. After following all the rules, what result did you
get? How about the others?
4. Why do we always obtain the same result which is
12?
Activity 2:
Plug It
This activity will help the
students recall how to find
the �-coordinate given an �-
coordinate in an equation
with two variables.
Duration: 10 minutes
Materials Needed: notebook, pen
Methodology:
1. Ask students to look for a pair.
2. Ask them to complete the table by finding the
corresponding value of � when �=2 for each of
the given equation below.
Equation � �
�=2�−3 2
�=�
2
−2�−1 2
�=�
3
+2�
2
−�−1 2
Expected Results:
Equation � �
�=2�−3 2 1
�=�
2
−2�−1 2 −1
�=�
3
+2�
2
−�−1 2 13
Guide Questions:
1. How were you able to solve the � value for each
item?
2. Look at the first equation in the table. What kind of
equation is this? How about the second and the
third one?
5
Guide Questions:
1. When is your birthday?
2. What number represents that month?
3. After following all the rules, what result did you
get? How about the others?
4. Why do we always obtain the same result which is
12?
Activity 2:
Plug It
This activity will help the
students recall how to find
the �-coordinate given an �-
coordinate in an equation
with two variables.
Duration: 10 minutes
Materials Needed: notebook, pen
Methodology:
1. Ask students to look for a pair.
2. Ask them to complete the table by finding the
corresponding value of � when �=2 for each of
the given equation below.
Equation � �
�=2�−3 2
�=�
2
−2�−1 2
�=�
3
+2�
2
−�−1 2
Expected Results:
Equation � �
�=2�−3 2 1
�=�
2
−2�−1 2 −1
�=�
3
+2�
2
−�−1 2 13
Guide Questions:
1. How were you able to solve the � value for each
item?
2. Look at the first equation in the table. What kind of
equation is this? How about the second and the
third one?
Unit 1: Introduction to Functions • Grade 11
6
B. Discussion
Suggested Instructional Flow
1. Define and Discover
• Function – a special kind of relation in which no two distinct ordered pairs have
the same first element
In an equation in two variables, � and �, the variable � may be expressed as �(�)
if every value of � corresponds to a single value of �.
The value that it takes in is called the input or independent variable while the
corresponding value that it produces is the output or dependent variable.
Example:
a. Suppose you are in a grocery store. Each grocery item has its corresponding
price. This is an example of a function wherein the independent variable is the
grocery item while the dependent variable is its price.
b. Let �(�)=3�−2, find �(2).
�(2)=3(2)−2
�(2)=4
Teacher’s Notes
An alternative way of presenting the following discussion is through the video lecture
included in your Quipper Video subscription package. Just log in to your teacher
account at www.link.quipper.com and assign your students the corresponding video
lecture which they can watch either at home or in the classroom.
Teacher’s Notes
A suggested warm-up activity with ICT integration is available in the presentation file
that you can download through this link: http://bit.ly/2S7UHxF
6
B. Discussion
Suggested Instructional Flow
1. Define and Discover
• Function – a special kind of relation in which no two distinct ordered pairs have
the same first element
In an equation in two variables, � and �, the variable � may be expressed as �(�)
if every value of � corresponds to a single value of �.
The value that it takes in is called the input or independent variable while the
corresponding value that it produces is the output or dependent variable.
Example:
a. Suppose you are in a grocery store. Each grocery item has its corresponding
price. This is an example of a function wherein the independent variable is the
grocery item while the dependent variable is its price.
b. Let �(�)=3�−2, find �(2).
�(2)=3(2)−2
�(2)=4
Teacher’s Notes
An alternative way of presenting the following discussion is through the video lecture
included in your Quipper Video subscription package. Just log in to your teacher
account at www.link.quipper.com and assign your students the corresponding video
lecture which they can watch either at home or in the classroom.
Teacher’s Notes
A suggested warm-up activity with ICT integration is available in the presentation file
that you can download through this link: http://bit.ly/2S7UHxF
Unit 1: Introduction to Functions • Grade 11
7
• Ways of Writing Functions
� (�)=2� +6 � is written as a function of �.
� →2� +6 The arrow is read as “is mapped to.”
�∶ � →2� +6 The colon symbol (:) is read as “such that.”
�={(�,�)|� =2�+6} The function � is written as a set.
Note that � and � are not fixed. We can use any letter we want. For instance, we
can use ??????(??????) to define a function that shows the distance ?????? traveled to be a
function of time ?????? spent traveling.
• Piecewise Function – a function composed of two or more expressions for the
different parts of the domain
Example:
Let �(�)={
3� if �<0
−1 if �=0
�
2
if �>0
The function � is a piecewise function because the set of possible values of the
independent variable has been divided into three parts: �>0,�=0, and �<0,
with each part having its own expression.
2. Develop and Demonstrate
The following examples may be used in the discussion.
Teacher’s Notes
Use slides 11-15 of the corresponding presentation file to present the worked
examples. You may also refer to the worked examples provided in the study
guide for varieties.
7
• Ways of Writing Functions
� (�)=2� +6 � is written as a function of �.
� →2� +6 The arrow is read as “is mapped to.”
�∶ � →2� +6 The colon symbol (:) is read as “such that.”
�={(�,�)|� =2�+6} The function � is written as a set.
Note that � and � are not fixed. We can use any letter we want. For instance, we
can use ??????(??????) to define a function that shows the distance ?????? traveled to be a
function of time ?????? spent traveling.
• Piecewise Function – a function composed of two or more expressions for the
different parts of the domain
Example:
Let �(�)={
3� if �<0
−1 if �=0
�
2
if �>0
The function � is a piecewise function because the set of possible values of the
independent variable has been divided into three parts: �>0,�=0, and �<0,
with each part having its own expression.
2. Develop and Demonstrate
The following examples may be used in the discussion.
Teacher’s Notes
Use slides 11-15 of the corresponding presentation file to present the worked
examples. You may also refer to the worked examples provided in the study
guide for varieties.
Unit 1: Introduction to Functions • Grade 11
8
Example 1: Consider an electric fan as a function machine. What you
do you think is the input, the function, and the output?
Solution/Explanation: Pressing any button on the electric fan (assuming it is
plugged into a power source) will cause the fan blade to
spin.
Hence, the buttons are the input, the spinning of the fan
blade is the function, and the wind it gives off is the
output.
Example 2: Consider the table of values below. Determine the input,
the function, and the output.
� −2 −1 0 1 2
� −4 −2 0 2 4
Solution/Explanation: The �-values (−2,−1,0,1,2) are the input. The �-values
(−4,−2,0,2,4) are the output.
Notice that if the value of � is −2, the value of � is −4. If �
is −1, � is −2, and so on.
By observing the pattern, note that each input is doubled
after “going through” the function. Hence, the function is
�=2�.
Example 3:
Let �(�)={
2�
2
if �<0
−1 if �=0
1−�
2
if �>0
. What is the function value
(output) if the given value of � is 2?
Solution/Explanation: To get the function value, first, identify which range the
input value �=2 falls within. Since 2>0, the function
that we should use is �(�)=1−�
2
.
8
Example 1: Consider an electric fan as a function machine. What you
do you think is the input, the function, and the output?
Solution/Explanation: Pressing any button on the electric fan (assuming it is
plugged into a power source) will cause the fan blade to
spin.
Hence, the buttons are the input, the spinning of the fan
blade is the function, and the wind it gives off is the
output.
Example 2: Consider the table of values below. Determine the input,
the function, and the output.
� −2 −1 0 1 2
� −4 −2 0 2 4
Solution/Explanation: The �-values (−2,−1,0,1,2) are the input. The �-values
(−4,−2,0,2,4) are the output.
Notice that if the value of � is −2, the value of � is −4. If �
is −1, � is −2, and so on.
By observing the pattern, note that each input is doubled
after “going through” the function. Hence, the function is
�=2�.
Example 3:
Let �(�)={
2�
2
if �<0
−1 if �=0
1−�
2
if �>0
. What is the function value
(output) if the given value of � is 2?
Solution/Explanation: To get the function value, first, identify which range the
input value �=2 falls within. Since 2>0, the function
that we should use is �(�)=1−�
2
.
Unit 1: Introduction to Functions • Grade 11
9
Simply plug in the value of � in the function to determine
the function value. That is,
�(2)=1−(2)
2
Then simplify.
�(2)=1−4
�(2)=−3
Therefore, the function value is −3 when �=2.
C. Practice and Feedback
For individual practice
1. Ask the students to answer the following problem items individually using pen and
paper.
2. Give students enough time to answer the problem items.
3. Call a random student to show his or her work on the board afterward.
4. Let the student share how he or she comes up with his or her solution.
5. Inform the student the accuracy of his answer and solution, and in the case when
there is some sort of misconception, lead the student to the right direction to find
the correct answer.
Problem 1: Consider a water dispenser as a function machine. What is
the input, the function, and the output?
Solution/Explanation: A water dispenser usually has two buttons (red and blue)
indicating whether you would want hot or cold water.
Teacher’s Notes
Use slides 16-17 of the corresponding presentation file to present the questions for
practice. You may also refer to theTry It Yourself! questions provided in the study
guide for varieties.
9
Simply plug in the value of � in the function to determine
the function value. That is,
�(2)=1−(2)
2
Then simplify.
�(2)=1−4
�(2)=−3
Therefore, the function value is −3 when �=2.
C. Practice and Feedback
For individual practice
1. Ask the students to answer the following problem items individually using pen and
paper.
2. Give students enough time to answer the problem items.
3. Call a random student to show his or her work on the board afterward.
4. Let the student share how he or she comes up with his or her solution.
5. Inform the student the accuracy of his answer and solution, and in the case when
there is some sort of misconception, lead the student to the right direction to find
the correct answer.
Problem 1: Consider a water dispenser as a function machine. What is
the input, the function, and the output?
Solution/Explanation: A water dispenser usually has two buttons (red and blue)
indicating whether you would want hot or cold water.
Teacher’s Notes
Use slides 16-17 of the corresponding presentation file to present the questions for
practice. You may also refer to theTry It Yourself! questions provided in the study
guide for varieties.
Unit 1: Introduction to Functions • Grade 11
10
Pressing any of these buttons will cause the dispenser to fill
your container with hot or cold water.
Hence, the buttons are the input, the process of filling your
container with hot or cold water is the function, and the hot
or cold water is the output.
Problem 2: Consider the table of values below. Determine the input, the
function, and the output.
� −2 −1 0 1 2
� −5 −2 1 4 7
Solution/Explanation: The �-values (−2,−1,0,1,2) are the input. The �-values
(−5,−2,1,4,7) are the output.
Notice that if the value of � is 2, the value of � is 7. If � is 1, �
is 4, and so on.
By observing the pattern, note that each input is tripled and
the result is increased by 1 after “going through” the function.
Hence, the function is �=3�+1.
Problem 3: Let �(�)=�
2
. What is �(−4)?
Solution/Explanation: Plug in −4 into the given function and then simplify.
�(−4)=(−4)
2
�(−4)=16
Hence, if �(�)=�
2
, then �(−4)=16.
10
Pressing any of these buttons will cause the dispenser to fill
your container with hot or cold water.
Hence, the buttons are the input, the process of filling your
container with hot or cold water is the function, and the hot
or cold water is the output.
Problem 2: Consider the table of values below. Determine the input, the
function, and the output.
� −2 −1 0 1 2
� −5 −2 1 4 7
Solution/Explanation: The �-values (−2,−1,0,1,2) are the input. The �-values
(−5,−2,1,4,7) are the output.
Notice that if the value of � is 2, the value of � is 7. If � is 1, �
is 4, and so on.
By observing the pattern, note that each input is tripled and
the result is increased by 1 after “going through” the function.
Hence, the function is �=3�+1.
Problem 3: Let �(�)=�
2
. What is �(−4)?
Solution/Explanation: Plug in −4 into the given function and then simplify.
�(−4)=(−4)
2
�(−4)=16
Hence, if �(�)=�
2
, then �(−4)=16.
Unit 1: Introduction to Functions • Grade 11
11
For group practice
1. Ask the students to form a minimum of 2 groups to a maximum of 5 groups.
2. Each group will answer problem items 4 and 5. These questions are meant to test
students’ higher-order thinking skills by working collaboratively with their peers.
3. Give students enough time to analyze the problem and work on their solution.
4. Ask each group to assign a representative to show their solution on the board and
discuss as a group how they come up with their solution.
5. Inform the student the accuracy of his answer and solution, and in the case when
there is some sort of misconception, give the student opportunity to work with
his/her peers to re-analyze the problem, and then lead them to the right direction to
find the correct answer.
Problem 4: Jocelyn bakes cookies. She sells these cookies online. She
earns ₱25 per cookie, but she incurs₱200 worth of expenses
per day. Using this scenario, answer the following:
a. Write a function relating her daily earnings or profit
??????(??????) and the number of cookies ?????? sold.
b. How many cookies does she need to sell for her to
break even? What does this imply?
Solution/Explanation: a. To determine her daily profit, we subtract her expenses
from her income. If ?????? represents the number of cookies
she can sell a day and each cookie is worth ₱25, then
her income is 25?????? a day. We subtract her expenses,
which is ₱200 from this expression.
??????(??????)=25??????−200
b. To break even means to neither earn nor lose money.
This means that ??????(??????)=0. Substituting this to the
function, we have the following solution:
0=25??????−200
200=25??????
200
25
=
25??????
25
8=??????
11
For group practice
1. Ask the students to form a minimum of 2 groups to a maximum of 5 groups.
2. Each group will answer problem items 4 and 5. These questions are meant to test
students’ higher-order thinking skills by working collaboratively with their peers.
3. Give students enough time to analyze the problem and work on their solution.
4. Ask each group to assign a representative to show their solution on the board and
discuss as a group how they come up with their solution.
5. Inform the student the accuracy of his answer and solution, and in the case when
there is some sort of misconception, give the student opportunity to work with
his/her peers to re-analyze the problem, and then lead them to the right direction to
find the correct answer.
Problem 4: Jocelyn bakes cookies. She sells these cookies online. She
earns ₱25 per cookie, but she incurs₱200 worth of expenses
per day. Using this scenario, answer the following:
a. Write a function relating her daily earnings or profit
??????(??????) and the number of cookies ?????? sold.
b. How many cookies does she need to sell for her to
break even? What does this imply?
Solution/Explanation: a. To determine her daily profit, we subtract her expenses
from her income. If ?????? represents the number of cookies
she can sell a day and each cookie is worth ₱25, then
her income is 25?????? a day. We subtract her expenses,
which is ₱200 from this expression.
??????(??????)=25??????−200
b. To break even means to neither earn nor lose money.
This means that ??????(??????)=0. Substituting this to the
function, we have the following solution:
0=25??????−200
200=25??????
200
25
=
25??????
25
8=??????
Unit 1: Introduction to Functions • Grade 11
12
Thus, she needs to sell at least 8 cookies per day to break
even. If she sells less than 8, then she loses money. On the
other hand, if she sells more than 8 cookies, then she earns
money.
Problem 5: In a university, mathematics grades are being converted in a
0.0 to 4.0 scale, with 4.0 being the highest and 0.0 being the
lowest. The conversion is given in the following table. Write a
function describing the conversion. Use ??????(�) to represent the
equivalent grade as a function of the raw grade �.
Raw Grade
(rounded off to an integer)
Equivalent
Grade
95 to 100 4.0
89 to 94 3.5
83 to 88 3.0
77 to 82 2.5
71 to 76 2.0
66 to 70 1.5
60 to 65 1.0
0 to 59 0.0
Solution/Explanation: The piecewise function that can represent the grades is given
below.
??????(�)=
{
4.0 ??????� 95≤�≤100
3.5 ??????� 89≤�≤94
3.0 ??????� 83≤�≤88
2.5 ??????� 77≤�≤82
2.0 ??????� 71≤�≤76
1.5 ??????� 66≤�≤70
1.0 ??????� 60≤�≤65
0.0 ??????� 0≤�≤59
12
Thus, she needs to sell at least 8 cookies per day to break
even. If she sells less than 8, then she loses money. On the
other hand, if she sells more than 8 cookies, then she earns
money.
Problem 5: In a university, mathematics grades are being converted in a
0.0 to 4.0 scale, with 4.0 being the highest and 0.0 being the
lowest. The conversion is given in the following table. Write a
function describing the conversion. Use ??????(�) to represent the
equivalent grade as a function of the raw grade �.
Raw Grade
(rounded off to an integer)
Equivalent
Grade
95 to 100 4.0
89 to 94 3.5
83 to 88 3.0
77 to 82 2.5
71 to 76 2.0
66 to 70 1.5
60 to 65 1.0
0 to 59 0.0
Solution/Explanation: The piecewise function that can represent the grades is given
below.
??????(�)=
{
4.0 ??????� 95≤�≤100
3.5 ??????� 89≤�≤94
3.0 ??????� 83≤�≤88
2.5 ??????� 77≤�≤82
2.0 ??????� 71≤�≤76
1.5 ??????� 66≤�≤70
1.0 ??????� 60≤�≤65
0.0 ??????� 0≤�≤59
Unit 1: Introduction to Functions • Grade 11
13
Performance Assessment
This performance assessment serves as formative assessment, divided into three sets
based on student’s level of learning. See next pages for separate printable worksheets.
• Worksheet I (for beginners)
• Worksheet II (for average learners)
• Worksheet III (for advanced learners)
Teacher’s Notes
For a standard performance assessment regardless of the student’s level of learning,
you may give the problem items provided in the Check Your Understanding section of
the study guide.
Web Box
On the following websites, you can find additional interactive questions and a calculator
about function notation and evaluating functions.
• Interactive Mathematics. "Introduction to Functions." Accessed January 27, 2019.
https://www.intmath.com/functions-and-graphs/1-introduction-to-functions.php
• Purple Math. "Function Notation and Evaluating at Numbers." Accessed January
27, 2019. https://www.purplemath.com/modules/fcnnot.htm
13
Performance Assessment
This performance assessment serves as formative assessment, divided into three sets
based on student’s level of learning. See next pages for separate printable worksheets.
• Worksheet I (for beginners)
• Worksheet II (for average learners)
• Worksheet III (for advanced learners)
Teacher’s Notes
For a standard performance assessment regardless of the student’s level of learning,
you may give the problem items provided in the Check Your Understanding section of
the study guide.
Web Box
On the following websites, you can find additional interactive questions and a calculator
about function notation and evaluating functions.
• Interactive Mathematics. "Introduction to Functions." Accessed January 27, 2019.
https://www.intmath.com/functions-and-graphs/1-introduction-to-functions.php
• Purple Math. "Function Notation and Evaluating at Numbers." Accessed January
27, 2019. https://www.purplemath.com/modules/fcnnot.htm
Unit 1: Introduction to Functions • Grade 11
14
Worksheet I
A. Given the following objects as “function machines,” identify the input, the function,
and the output. (6 points)
1. Guitar
Input: ________________________
Function: ________________________
Output: ________________________
2. Elevator
Input: ________________________
Function: ________________________
Output: ________________________
B. Find the function value (output) given the value of � (input). (10 points)
1. �(�)=�−2; �=5 2. �(�)=�
2
+1; �=−1
3. ℎ(�)=�
3
; �=−2 4. �(�)=−3�;�=0
5. �(�)=3�+4; �=2
14
Worksheet I
A. Given the following objects as “function machines,” identify the input, the function,
and the output. (6 points)
1. Guitar
Input: ________________________
Function: ________________________
Output: ________________________
2. Elevator
Input: ________________________
Function: ________________________
Output: ________________________
B. Find the function value (output) given the value of � (input). (10 points)
1. �(�)=�−2; �=5 2. �(�)=�
2
+1; �=−1
3. ℎ(�)=�
3
; �=−2 4. �(�)=−3�;�=0
5. �(�)=3�+4; �=2
Unit 1: Introduction to Functions • Grade 11
15
C. Analyze and solve the problem below.
Gyra needs to buy bags for her outreach program. She went to a bargain market to
look for the best deal she can get. She found out that Aling Zeny’s store gives the
best deal. Aling Zeny, the owner of the store, gave the following quotation:
a. If she buys at most 20 bags, each bag would cost ₱200 each.
b. If she buys 21-50 bags, each bag would cost ₱180 each.
c. If she buys at least 51 bags, each bag would cost ₱150 each.
1. Write a function relating the total cost ??????(??????) and the number of bags ?????? bought. (2
points)
Solution and answer:
2. If she intends to buy 30 bags, how much would that cost? (2 points)
Solution and answer:
15
C. Analyze and solve the problem below.
Gyra needs to buy bags for her outreach program. She went to a bargain market to
look for the best deal she can get. She found out that Aling Zeny’s store gives the
best deal. Aling Zeny, the owner of the store, gave the following quotation:
a. If she buys at most 20 bags, each bag would cost ₱200 each.
b. If she buys 21-50 bags, each bag would cost ₱180 each.
c. If she buys at least 51 bags, each bag would cost ₱150 each.
1. Write a function relating the total cost ??????(??????) and the number of bags ?????? bought. (2
points)
Solution and answer:
2. If she intends to buy 30 bags, how much would that cost? (2 points)
Solution and answer:
Unit 1: Introduction to Functions • Grade 11
16
Worksheet II
A. Find the function value (output) given the value of � (input). (10 points)
1. �(�)=3�−2; �=2 2. �(�)=�
2
+2�−3; �=−2
3. ℎ(�)=�
3
+�
2
; �=−3 4. �(�)=3�
3
; �=0
5. �(�)=3�
2
+7; �=4
B. Determine whether � can be expressed as a function of � in the given equation.
Write F if it can be expressed as a function and N if it is not on the space provided
before the number. (5 points)
____1. �=5�−7
____2. �=�
2
−3�−2
____3. �
2
=�+7
____4. 3�=5�+2
____5. �
3
+�
2
+3=�
16
Worksheet II
A. Find the function value (output) given the value of � (input). (10 points)
1. �(�)=3�−2; �=2 2. �(�)=�
2
+2�−3; �=−2
3. ℎ(�)=�
3
+�
2
; �=−3 4. �(�)=3�
3
; �=0
5. �(�)=3�
2
+7; �=4
B. Determine whether � can be expressed as a function of � in the given equation.
Write F if it can be expressed as a function and N if it is not on the space provided
before the number. (5 points)
____1. �=5�−7
____2. �=�
2
−3�−2
____3. �
2
=�+7
____4. 3�=5�+2
____5. �
3
+�
2
+3=�
Unit 1: Introduction to Functions • Grade 11
17
C. Analyze and solve the problem below.
Kristoffer needs to buy t-shirts for an event. He went to a bargain market to look for
the best deal he can get. He found out that Elly Store gives the best deal. Elly, the
owner of the store, gave the following quotation:
i. If he buys at most 100 t-shirts, each t-shirt would cost ₱150 each.
ii. If he buys 101-200 t-shirts, each t-shirt would cost ₱130 each.
iii. If she buys at least 201 t-shirts, each t-shirt would cost ₱110each.
1. Write a function relating the total cost ??????(??????) and the number of t-shirts ?????? bought.
(2 points)
Solution and answer:
2. If he intends to buy 120 shirts, how much would that cost? (3 points)
Solution and answer:
17
C. Analyze and solve the problem below.
Kristoffer needs to buy t-shirts for an event. He went to a bargain market to look for
the best deal he can get. He found out that Elly Store gives the best deal. Elly, the
owner of the store, gave the following quotation:
i. If he buys at most 100 t-shirts, each t-shirt would cost ₱150 each.
ii. If he buys 101-200 t-shirts, each t-shirt would cost ₱130 each.
iii. If she buys at least 201 t-shirts, each t-shirt would cost ₱110each.
1. Write a function relating the total cost ??????(??????) and the number of t-shirts ?????? bought.
(2 points)
Solution and answer:
2. If he intends to buy 120 shirts, how much would that cost? (3 points)
Solution and answer:
Unit 1: Introduction to Functions • Grade 11
18
Worksheet III
A. Determine whether the given scenario is a function. Write F if it is a function and N if
it not on the space provided before the number. (5 points)
____1. Each student is associated with his/her favorite color/s.
____2. Each student is associated with his/her country of origin.
____3. Each student is mapped to the number of countries he/she has visited.
____4. Each e-mail address is paired with a password.
____5. Each person is mapped to his/her favorite movie/s.
B. Evaluate each function at the given the value of �. (5 points)
1. �(�)=�
3
−�−2; �=5 2. �(�)=�
2
+�−1; �=−1
3. ℎ(�)=|�|−3; �=−2
4. �(�)={
1 ??????� �≤0
4� ??????� �>0
; �=0
5. �(�)=�
3
+�
2
+3; �=2
18
Worksheet III
A. Determine whether the given scenario is a function. Write F if it is a function and N if
it not on the space provided before the number. (5 points)
____1. Each student is associated with his/her favorite color/s.
____2. Each student is associated with his/her country of origin.
____3. Each student is mapped to the number of countries he/she has visited.
____4. Each e-mail address is paired with a password.
____5. Each person is mapped to his/her favorite movie/s.
B. Evaluate each function at the given the value of �. (5 points)
1. �(�)=�
3
−�−2; �=5 2. �(�)=�
2
+�−1; �=−1
3. ℎ(�)=|�|−3; �=−2
4. �(�)={
1 ??????� �≤0
4� ??????� �>0
; �=0
5. �(�)=�
3
+�
2
+3; �=2
Unit 1: Introduction to Functions • Grade 11
19
C. Determine whether � can be expressed as a function of � in the given equation.
Write F if it can be expressed as a function and N if it is not on the space provided
before the number. (5 points)
____1.�=|�−2|
____2.|�+2|=�
____3.�
2
+�
2
=1
____4.�
3
−�=�
____5.�
3
=�
D. Analyze and solve the problem below.
Kristelneeds to buy notebooks for her outreach program. She went to a bargain market
to look for the best deal she can get. She found out that Aling Zeny’s store gives the
best deal. Aling Zeny, the owner of the store, gave the following quotation:
i. If she buys at most 20 notebooks, each notebook would cost ₱20 each.
ii. If she buys 21-50 notebooks, each notebook would cost ₱18 each.
iii. If she buys at least 51 notebooks, each notebook would cost ₱15 each.
1. Write a function relating the total cost ??????(??????) and the number of notebooks ??????
bought. (2 points)
Solution and answer:
2. If she intends to spend ₱900 for notebooks, what is the maximum number of
notebooks she can buy? (3 points)
Solution and answer:
19
C. Determine whether � can be expressed as a function of � in the given equation.
Write F if it can be expressed as a function and N if it is not on the space provided
before the number. (5 points)
____1.�=|�−2|
____2.|�+2|=�
____3.�
2
+�
2
=1
____4.�
3
−�=�
____5.�
3
=�
D. Analyze and solve the problem below.
Kristelneeds to buy notebooks for her outreach program. She went to a bargain market
to look for the best deal she can get. She found out that Aling Zeny’s store gives the
best deal. Aling Zeny, the owner of the store, gave the following quotation:
i. If she buys at most 20 notebooks, each notebook would cost ₱20 each.
ii. If she buys 21-50 notebooks, each notebook would cost ₱18 each.
iii. If she buys at least 51 notebooks, each notebook would cost ₱15 each.
1. Write a function relating the total cost ??????(??????) and the number of notebooks ??????
bought. (2 points)
Solution and answer:
2. If she intends to spend ₱900 for notebooks, what is the maximum number of
notebooks she can buy? (3 points)
Solution and answer:
Unit 1: Introduction to Functions • Grade 11
20
Answer Key
Worksheet I
A. 1. Input: Chords; Function: Strumming of the string; Output: Tune or Music
2. Input: Buttons; Function: Elevator moving up or down; Output: Floor destination
B. 1. 3
2. 2
3. −8
4. 0
5. 10
C. 1. ??????(??????)={
200?????? if 0≤??????≤20
180?????? if 21≤??????≤50
150?????? if ??????≥51
2. ₱5 400
Worksheet II
A. 1. 4
2. −3
3. −18
4. 0
5. 55
B. 1. F
2. F
3. N
4.F
5. F
C. 1. ??????(??????)={
150?????? if 0≤??????≤100
130?????? if 101≤??????≤200
110?????? if ??????≥201
2. ₱15 600
20
Answer Key
Worksheet I
A. 1. Input: Chords; Function: Strumming of the string; Output: Tune or Music
2. Input: Buttons; Function: Elevator moving up or down; Output: Floor destination
B. 1. 3
2. 2
3. −8
4. 0
5. 10
C. 1. ??????(??????)={
200?????? if 0≤??????≤20
180?????? if 21≤??????≤50
150?????? if ??????≥51
2. ₱5 400
Worksheet II
A. 1. 4
2. −3
3. −18
4. 0
5. 55
B. 1. F
2. F
3. N
4.F
5. F
C. 1. ??????(??????)={
150?????? if 0≤??????≤100
130?????? if 101≤??????≤200
110?????? if ??????≥201
2. ₱15 600
Unit 1: Introduction to Functions • Grade 11
21
Worksheet III
A. 1. N
2. F
3. F
4. F
5. N
B. 1. 118
2. −1
3. −1
4. 1
5. 15
C. 1. F
2. N
3. N
4. F
5. F
D. 1. ??????(??????)={
20?????? if 0≤??????≤20
18?????? if 21≤??????≤50
15?????? if ??????≥51
2. 60 notebooks
21
Worksheet III
A. 1. N
2. F
3. F
4. F
5. N
B. 1. 118
2. −1
3. −1
4. 1
5. 15
C. 1. F
2. N
3. N
4. F
5. F
D. 1. ??????(??????)={
20?????? if 0≤??????≤20
18?????? if 21≤??????≤50
15?????? if ??????≥51
2. 60 notebooks
Unit 1: Introduction to Functions • Grade 11
22
Synthesis
Wrap-up
To summarize the lesson, ask students the following
questions:
1. What is a function?
2. How do we denote functions?
Application and Values
Integration
To integrate values and build connection to the real world,
ask students the following questions:
1. Why are functions important in our life?
2. How do we make use of functions in our life?
Bridge to the Next Topic To spark interest for the next lesson, ask students the
following questions:
1. What do we call relationships that are not functions?
2. How do we determinea function given its graph?
Bibliography
Cabral, Emmanuel, et al. Precalculus. Quezon City: Ateneo de Manila University Press, 2010.
Lumen. "Introduction to Function." Accessed January 27, 2019.
https://courses.lumenlearning.com/boundless-algebra/chapter/introduction-to-
functions/
NCTM. "Magic Numbers." Accessed January 27, 2019.
http://figurethis.nctm.org/challenges/c60/challenge.htm
Versora, Debbie Marie, et al. Teaching Guide for Senior High School General Mathematics Core
Subject. Quezon City: Commission on Higher Education, 2016.
22
Synthesis
Wrap-up
To summarize the lesson, ask students the following
questions:
1. What is a function?
2. How do we denote functions?
Application and Values
Integration
To integrate values and build connection to the real world,
ask students the following questions:
1. Why are functions important in our life?
2. How do we make use of functions in our life?
Bridge to the Next Topic To spark interest for the next lesson, ask students the
following questions:
1. What do we call relationships that are not functions?
2. How do we determinea function given its graph?
Bibliography
Cabral, Emmanuel, et al. Precalculus. Quezon City: Ateneo de Manila University Press, 2010.
Lumen. "Introduction to Function." Accessed January 27, 2019.
https://courses.lumenlearning.com/boundless-algebra/chapter/introduction-to-
functions/
NCTM. "Magic Numbers." Accessed January 27, 2019.
http://figurethis.nctm.org/challenges/c60/challenge.htm
Versora, Debbie Marie, et al. Teaching Guide for Senior High School General Mathematics Core
Subject. Quezon City: Commission on Higher Education, 2016.
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