Week 3 Day 2L8 (Subtask 1)

MATHEMATICS RESOURCE PACKAGE
QUARTER I
Week 3
Subject:
GENERAL Grade Level: 11
MATHEMATICS
Date: ________ Day: 2 (subtask 1 of Lesson 8)
Content Standard The learner demonstrates understanding of key concepts of rational functions.
Performance The learner is able to accurately formulate and solve real-life problems
Standard involving rational functions.
Learning M11GM-Ic-2
Competency The learner graphs rational functions.
I. OBJECTIVES
Knowledge: Identifies the x and y intercepts to be used in graphing rational functions;
Skills: Graphs rational functions;
Affective: Shows patience in graphing rational functions.
II. CONTENT Graphing Rational Functions
III. LEARNING RESOURCES
A. References
1. Teacher’s TG for SHS General Mathematics, pp. 50-63
Guide Pages
2. Learner’s LM in General Mathematics, pp. 44-56
Materials
Pages
3. Textbook General Mathematics by Orlando Oronce Series 2016
Pages
4. Additional Slide Decks on the Topic
Materials
5. Learning Teacher’s Guide and Learner’s Material
Resources
(LR) portal
B. Other Learning General Mathematics Diwa Publishing , 2016
Resources
IV. PROCEDURES
A. Reviewing or
Recall the previous discussion in finding the domain, range, intercepts, zeroes
presenting the
and asymptotes of rational functions.
new lesson
Prepared by: Mercyditha D. Enolpe

SHS Teacher (JMLMHS)
B. Establishing a
purpose for the
lesson
Figure: Zeroes and asymptotes of f(x).

Ask: What have you observed on the graph?
Allow learners to discuss the graph.
Discuss the steps in graphing a simple rational function and develop a
process for graphing other rational functions.
C. Presenting In sketching the graph of a rational function, we will make use of the x and y-
examples of the intercepts of the function. In addition, we will observe how the function
new lesson behave near the values the function in undefined, as well as in the extreme
values of x.
D. Discussing new
concepts and
practicing new
skills #1
The numerator x-2 will be zero at x = 2. Therefore x = 2 is zero of f(x0. Since

it is a real zero, it is also an x-intercept.
−2
The y-intercept of a function is equal to f(0) = = −1.
2

E. Discussing new
concepts and Say: Observe that as x approaches -2 from the left and from the right, the
practicing new grpah gets closer and closer to the line x = -2, indicated n the figure with a
skills #2 dashed line. We call thins line a vertical asymptote.
Definition.
The vertical line x= a is a vertical asymptote of a function f if the graph of f
either increases or decreases without bound as the x-values approach a from
the right or left.
Definition.
The horizontal line y = b is a horizontal asymptote of a function f if the
graph of f(x) gets closer to b as x increases or decreases without bound
(x→+∞ 𝑜𝑟 𝑥 → −∞).

F. Developing
Mastery
G. Finding
practical
applications of
concepts and
skills in daily
living
H. Making Ask: How are you going to graph rational functions?
Generalizations The definition of the following terms are emphasized here.
and abstractions  vertical asymptote
about the lesson  horizontal asymptote
 Finding the x- and y-intercepts
I.Evaluating learning See Attachment.
J. Additional
Activities for
application or
remediation
V. REMARKS
VI. REFLECTION
A. No. of learners who A. ____ No. of learners who earned 80% in the evaluation
earned 80% in the
evaluation
B. No. of learners who B. ____ No. of learners who require additional activities for
require additional activities remediation
for remediation
C. Did the remedial lessons C. Did the remedial lessons work? _____ No. of learners who have
work? No. of learners who caught up the lesson.
have caught up the lesson
D. No. of learners who D. ___ No. of learners who continue to require remediation
continue to require
remediation
E. Which of my teaching Strategies used that work well:
strategies worked well? ___ Group collaboration ___ Games ___ Poweerpoint presentation
Answering preliminary activities/exercises
Why did these work? ___ Discussion ___ Differentiated Instruction
___ Case Method ___Role Playing /Drama
___ Think-Pair-Share (TPS) ___ Doscivery Method

___ Rereading of Paragraphs/Poems/Stories ___ Lecture Method
Why?
___ Complete Ims
___ Availability of Materials
___ Pupil’s eagerness to learn
___ Group member’s cooperation in doing their tasks
F. What difficulties did I ___ Bullying among learners ___ Equipment (AVR/LCD)
encounter which my ___ Learner’s behavior/attitude ___ Science/Computer/Internet Lab
___ Colorful Ims ___ Additional Clerical Works
principal and supervisor ___ Unavaailable Technology ___ Reading Readiness
help me solve?
G. What innovation or
localized I used/discover
which I wish to share with
other teacher?

EVALUATION
WORKSHEET _____
3𝑥 2 −8𝑥−3
1. Sketch the graph of (x) = 2𝑥 2 +7𝑥−4,find its domain and range.
Answer. 1.

Additional Activity (if necessary)
Instruction:
Sketch the graph of the following rational functions. Identify the x and y-intercepts, the asymptotes.
2𝑥+3 𝑥 2 −𝑥+6
1. f(x) = 2. f(x) = 𝑥 2 −6𝑥+8
4𝑥−7


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MATHEMATICS RESOURCE PACKAGE

III. LEARNING RESOURCES

Prepared by: Mercyditha D. Enolpe

Figure: Zeroes and asymptotes of f(x).

The numerator x-2 will be zero at x = 2. Therefore x = 2 is zero of f(x0. Since

Prepared by: Mercyditha D. Enolpe

Prepared by: Mercyditha D. Enolpe

Prepared by: Mercyditha D. Enolpe

Prepared by: Mercyditha D. Enolpe

Prepared by: Mercyditha D. Enolpe

Additional Activity (if necessary)

Prepared by: Mercyditha D. Enolpe

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