School PAKU NATIONAL HIGH SCHOOL
Teacher MARIETA M. CADAY
GRADE 8
DAILY LESSON LOG
Grade Level 8
Learning Area MATHEMATICS
Teaching Dates and Time DAY 1
Quarter SECOND
Session 1
I. OBJECTIVES
1. Content Standards
The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic
expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities
in two variables and linear functions.
2. Performance Standards The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic
expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities
in two variables and linear functions, and solve these problems accurately using
a variety of strategies.
3. Learning Competencies / Finds the domain and range of a function.
(M8AL-IId-1 )
Objectives
a. Identify the domain and range of a function given equation
b. Describe the domain and range of a function given the equation.
c. Appreciate the concept of domain and range in real-life situation.
II. CONTENT
DOMAIN AND RANGE OF A FUNCTION
III. LEARNING RESOURCES
A. References
1.
Teacher’s Guide
pages
175-180
2.
Learner’s Materials
pages
158-161
3.
Textbook
Additional Materials http://www.mathaids.com/Algebra/Algebra_1/Domain_Range/
http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U17_L2_T3_t
from Learning
Resource (LR) portal ext_final.html
http://coachgriffin.weebly.com/uploads/2/4/6/5/24656764/day_12__4.5_day_2_notes_-_key.pdf
https://www.youtube.com/watch?v=fyROLkZc7E
http://www.intmath.com/functions-and-graphs/2a-domain-and-range.php
https://courses.lumenlearning.com/collegealgebra1/chapter/find-domain-and-range-from-graphs/
Grade 8 LCTG by DepEd Mathematics Cavite 2016
B. Other Learning
Laptop, monitor
Resources
4.
IV. PROCEDURES
A. Reviewing previous lesson
or presenting the new
lesson
Preliminaries
Identify the domain and
range of the following:
1. {(-1,3), (0,1), (1,-1),
(2,-3), (3,-5)}
2. {(0,2),(1,3),(2,4),
(3,5),(4,6)}
3.
4.
B. Establishing a purpose for
the lesson
1. How do you identify
domain and range?
2. How will you identify
domain and range of an
equation?
C. Presenting examples/
instances of the lesson
Given the rule, we can find
the domain and range of a
function algebraically.
Examples:
1. Consider the function
f (x) x 1.
We can substitute x with any real number that does not make the function undefined. Therefore, the
domain is the set of real numbers. To find range, we let y f (x) x 1 and solve for x in terms of y.
Thus, x y 1 or x y 1; which can be defined for any real number y.
Therefore, the range of
f ( x)  x 2  3 x  2
f (x) is the set of real numbers.
2. If the function is in the form of a quotient like
,
4
x  4to take note that rational expression should not have the denominator zero, therefore, 𝑥 here
We have
f ( x) 
should not be equal to 4, but other real numbers can be possible value of 𝑥.
To find the range, let
4
f ( x) 
x  4 and then solve for 𝑥 in terms of 𝑦. Solving for
4 y  4 , which is
x
y
undefined for 𝑦 = 0. Therefore, the range consists of nonzero real numbers.
3. If the function is in the form of radical with an even number index as in
f (x) x 3 ,
Since the radicand must not be negative, we set
x 3 0. This will give
x 3.
Therefore,
D x / x 3 =3,.
For the range, we solve the equation, y x 3 for 𝑥 in terms of y 0,
(y)2= (x+3)2
y2x 3
Therefore, x= y2-3.The resulting equation tells that y2 - 3 will always be defined for any
real number 𝑦, but the original equation
y = x + 3 means that 𝑦 is the principal square root of 𝑥 + 3, so 𝑦 is never negative. Therefore, the range is
R y / y 0 ,
0, .
D. Discussing new concepts 1. How can you describe the domain and range of a function given the equation?
and practicing new skills #1 2. Is it necessary that you have knowledge in algebraic solution of equations to find the domain and range given the function
in the form of equation?
E. Discussing new concepts
and practicing new skills #2
Determine the domain and the range of the following function.
1. f(x)= x + 4
2. f ( x)  x  2
3
3. f ( x) 
x2
F. Developing mastery
(Leads to Formative Assessment
3)
F. Finding practical
applications of concepts
and skills in daily living
G. Making generalizations and
abstractions about the
lesson
H. Evaluating learning
Determine the domain and the range of the following function.
1.f(x)=x + 10
2. f(x)=√3−s
3. f(x)= x -2
Identify the domain and range of f(x) = x -5, then sketch the graph of a function.
Generalization:
The domain of a function is the set of all possible values of its first coordinates and the range is the set
of all possible values of its second coordinates.
The domain and range of a function or relation maybe identified from the set of ordered pairs, from mapping
diagram, from the graph or from a rule or equation.
Give 5 relations that are function. You may express them as ordered pairs, mapping, graph, or rule or
equation. Determine the domain and range of the functions you have made .
I. Additional activities for
application or remediation
1. Follow Up:
Find the domain and range of each function.
1. f(x)= x- 7
2. f ( x) 
3x
x 1
2. Study:
Define a linear function.
Reference: Learner’s Module pages 172 – 177
V. REMARKS
VI. REFLECTION
1. No.of learners who earned
80% on the formative
assessment
2. No.of learners who require
additional activities for
remediation.
3. Did the remedial lessons
work? No.of learners who
have caught up with the
lesson.
4. No.of learners who continue
to require remediation
5. Which of my teaching
strategies worked well? Why
did these work?
6. What difficulties did I
encounter which my
principal or supervisor can
help me solve?
7. What innovation or localized
materials did I use/discover
which I wish to share with
other teachers?