Grade 12 School MANICAHAN NATIONAL HIGH SCHOOL Grade Level GRADE 11

DAILY LESSON LOG Teacher JELA MARIE C. ESCUDERO Learning Area GENERAL MATHEMATICS
Teaching Dates and Time MONDAY, JUNE 10, 2019 Semester FIRST

I. OBJECTIVES
A. Content Standards The learner demonstrates understanding of key concepts offunctions.
B. Performance Standards The learner is able to accurately constructmathematical models to represent real-life situations using functions.
C. Learning Competencies/Objectives The learner
Write with LC Code for each 1. represents real-life situations using functions, including piece-wise functions. M11GM-Ia-1
2. solves problems involving functions. M11GM-Ia-4
II. CONTENT
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide pages Pg. 2-10
2. Learner’s Materials pages
3. Textbook pages
4. Additional Materials from Learning Resource (LR) portal
B. Other Learning Resources
IV. PROCEDURES
A. Reviewing previous lesson or presenting the new lesson I gave you an assignment to look for the definition of relation and function. (using the index card, the teacher will randomly choose some students to recite)
Definition: A relation is a rule that relates values from a set of values (called the domain) to a second set of values (called the range). A relation is a set of ordered pairs (x,y).
Definition: A function is a relation where each element in the domain is related to only one value in the range by some rule. A function is a set of ordered pairs (x,y) such that no two ordered pairs
have the same x-value but different y-values. Using functional notation, we can write f(x) = y, read as “f of x is equal to y.” In particular, if (1, 2) is an ordered pair associated with the function f,
then we say that f(2) = 1
B. Establishing a purpose for the lesson We will start our lesson with chapter 1, Functions. These definitions will guide you along the way.
C. Presenting examples/instances of the new lesson Example 1. Which of the following relations are functions?
F={(1,2),(3,4),(5,6),(7,8)}
G={(1,3),(1,4),(2,5),(2,6)}
H={(1,3),(2,6),(3,9),…, (n,3n), ….}
Example 2. Which of the following mapping diagrams represent functions?

D. Discussing new concepts and practicing new skills #1 The relations f and h are functions because no two ordered pairs have the same x-value but different y-values. Meanwhile, g is not a function because (1,3) and (1,4) are ordered pairs with the
same x-value but different y-values.Relations and functions can be represented by mapping diagrams where theelements of the domain are mapped to the elements of the range using arrows. In
this case, the relation or function is represented by the set of all the connections represented by the arrows.
E. Discussing new concepts and practicing new skills #2 The relations f and g are functions because each value y in Y is unique for a specific value of x. The relation h is not a function because there is at least one element in X for which there is more
than one corresponding y-value. For example, x=7 corresponds to y = 11 or 13. Similarly, x=2 corresponds to both y=17 or 19. A relation between two sets of numbers can be illustrated by a
graph in the Cartesian plane, and that a function passes the vertical line test.
The Vertical Line Test
A graph represents a function if and only if each vertical line intersects the graph at most
F. Developing mastery Identify the domain for each relation using set builder notation.
(Leads to Formative Assessment 3)
G. Finding practical applications of concepts and skills in daily living Functions can often be used to model real situations. Identifying an appropriate functional model will lead to a better understanding of various phenomena.
Example Give a function C that can represent the cost of buying x meals, if one meal costs P40.
Solution. Since each meal costs P40, then the cost function is C(x) = 40x.
Example One hundred meters of fencing is available to enclose a rectangular area next to a river (see figure). Give a function A that can represent the area that can be enclosed, in terms of x.
Solution. The area of the rectangular enclosure is A = xy. We will write this as a function of x. Since only 100 m of fencing is available, then x + 2y = 100 or y = (100 – x)/2 = 50 – 0.5x. Thus, A(x)
= x(50 – 0.5x) = 50x – 0.5x2.
H. Making generalizations and abstractions about the lesson Relations are rules that relate two values, one from a set of inputs and the second from the set of outputs.
Functions are rules that relate only one value from the set of outputs to a value from the set of inputs.
I. Evaluating learning 1. Is the relation {(0,0), (1,1), (2,4), (3,9), … (n, n2 ), …} a function?
2. Which of the following diagram represents a relation that is NOT a function?

3.Can the graph of a circle be considered a function?

4. Give the domain of y=sqrt of (2-x) using set builder notation.
5. Contaminated water is subjected to a cleaning process. The concentration of pollutants is initially 10 mg per liter of water. If the cleaning process can reduce the pollutant by 5% each hour,
define a function that can represent the concentration of pollutants in the water in terms of the number of hours that the cleaning process has taken place.
J. Additional activities for application or remediation
V. REMARKS
VI. REFLECTION
A. No. of learners who earned 80% on the formative assessment
B. No. of learners who require additional activities for remediation.
C. Did the remedial lessons work? No. of learners who have caught up with the lesson.
D. No. of learners who continue to require remediation.
E. Which of my teaching strategies worked well? Why did these work?
F. What difficulties did I encounter which my principal or supervisor can help me solve?
G. What innovation or localized materials did I use/ discover which I wish to share with other
teachers?
Noted:

EMELDA G. MONDEJAR, Ed.D.

School Principal II