asian-university.org · web view[name of program: access academy] [course code – math0100:...

[NAME OF PROGRAM: ACCESS ACADEMY]

[COURSE CODE – MATH0100: COURSE NAME – PRECALCULUS]

ACADEMIC YEAR 2018-2019[SEMESTER – Fall ]

COURSE SYLLABUS

1. COURSE INFORMATION

Classes held: 29 August, 2018 Credits : 4Prerequisite: Higher Secondary Mathematics

2. FACULTY INFORMATION

Faculty Name: Faiz AhmadEmail: [email protected] Location: H 518Office Hours: 4 Hours

Qualifications: M.Sc. in Physics, University of Chittagong, Bangladesh B.Sc. in Physics, University of Chittagong, Bangladesh

Areas of Expertise: Pre-calculus, Calculus, Newtonian Mechanics, Nuclear Physics, and Astrophysics.

Profile:

Faiz served as a Senior Instructor in Mathematics, Pathways for Promise at AUW from Summer II 2016 to Fall 2017 and then in AA as Instructor (Pre-Calculus) during 2018 Spring Semester. He graduated from the University of Chittagong (Bangladesh), in Physics with both first class results. Before joining AUW, he worked for Presidency International School (Cambridge affiliated) and Bangladesh Elementary School (NC English medium) for 5 years. He actively participated in numerous training sessions conducted by local and international experts on teaching methods, lesson planning, class room management, student psychology etc. He is also one of the 29 listed junior researchers from South Asia selected by NABIC & BCAS (Dhaka) and NERSC (Bergen, Norway). In 2017 he successfully completed AuthorAID (based in Oxford, UK) grant proposal and research writing online course and obtained Merit grade.

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3. TEXT AND OTHER COURSE MATERIALS

Required Text: Michael Sullivan Pre-calculus.Other necessary course materials will be providing in the class room.

4. COURSE OBJECTIVES AND DESCRIPTION

Course Description: Pre-calculus is a one year course of mathematics. Pre-calculus exposes

students to a rigorous level of mathematics, essential to the study of UG level courses under

Liberal arts and Sciences. The pace of the class and depth of the material may be different than

those encountered in previous education. The focus of this course is primarily on various types

of functions: polynomial, rational, exponential, logarithmic and trigonometric. The student will

also learn about the behavior of functions through graphs and transformations; they will gain

insight into the properties of these functions and their inverse forms. At the end of the course,

students will be able to apply a variety of techniques to abstract and real-life problems alike.

They will also use "Khan Academy Videos/ Resources" in this course in a blended learning and

assessing approach.

Course Objectives:

1. Gaining factual knowledge (Essential)

2. Learning fundamental principles, generalizations or theories (Important)

3. Learning to apply course material (to improve thinking, problem solving, and decisions) (Important)

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[Fall Semester]

Learning Goals

Graphs

o Graphs of Equations in Two Variables

o Lines

Functions and their Graphs

o Functions

o The Graph of a Function

o Properties of Functions

o Transformations

Linear and Quadratic Functions

o Linear Functions and Their Properties

o Building Linear Functions from Data

o Quadratic Functions and Their Properties

o Building Quadratic Functions from Data

o Inequalities Involving Quadratic Functions

Polynomial and Rational Functions

o Polynomial Functions and Models

o Properties of Rational Functions

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5. LEARNING OUTCOMES

Student Learning Outcomes Method of Assessment1) Demonstrate the fundamental concept of a mathematical function and all of its properties.

Quiz based upon class lecturer, Assigned homework exercises, and exam.

2) Solve equations and inequalities both algebraically and graphically.


3) Find zeros of polynomials and the zero product property.


4) Graph polynomial, absolute value, square root, rational function and polynomial functions.


5)Identify some connection between the mathematics at this level and the real world


6. ATTENDANCE REQUIREMENT & GRADING POLICY

An “A” designates truly excellent and outstanding work and an “F” represents complete lack of effort resulting in unacceptable work.

A+ 4.3 (96.68-100) A 4.0 (93.33-96.67) A- 3.7 (90.00-93.32)

B+ 3.3 (86.68-89.99) B 3.0 (83.33-86.67) B- 2.7 (80.00-83.32)

C+ 2.3 (76.68-79.99) C 2.0 (73.33-76.67) C- 1.7 (70.00-73.32) *

D+ 1.3 (66.68-69.99) D 1.0 (63.33-66.67) D- 0.7 (60.00-63.32)

F 0 (59 .99 or below)

* Any grade below C- (70%) requires remedial work. A course of action will be decided in agreement between the student, teacher, and an academic administrator.

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7. CONTACT WITH YOUR PROFESSOR

If you face any problem you can contact me during my office hours or by appointment.Students are expected to check their email at least twice daily, preferably in the morning and evening. Students are advised that a majority of faculty answer email within a 24 hour period during the week and a 48 hour period during weekends. Please be aware that students who do not check email regularly may miss important class announcements.

8. COURSE SCHEDULE

*Please see Khan Academy Video links provided at last 5 pages of this plan booklet. Also, note that you can watch much more that fits our lesson objectives and we may update (include/exclude) the list as Khan Academy also uploads new videos time to time and to make the links more useful for our students and lesson. I may send you all the links in your email as well so that you can click and go to the link directly.

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Fall Semester Pre-Calculus Lesson Plan

Week 1

1st class 2nd class 3rd class Objectives Mathematics

Placement Test Introducing the Fall Syllabus Familiar with rectangular coordinate system

Use the Distance Formula

Use the Midpoint Formula

Class Outline

N/ASome basics discussion, for instance, finding area of circle geometrically, proving Pythagorean theorem, defining undefined, zero and infinity, some puzzle problems

Proof of Mid-Point and Distance formula,Doing some examples on Midpoint and Distance formula,

Handouts N/ASyllabus

None

Homework N/A None Some problems from Exercise 1

Evaluation N/A N/A Get some problems done by students from exercise.

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Pre-Calculus Lesson Plan

Week 2

1st class 2nd class 3rd class Objectives Graph Equation by

plotting points

Find intercept from graph

Find intercepts from equation

Understanding Symmetry concept

Test equation for symmetry w.r.t x-axis, y-axis and origin

To graph some important equations

Class Outline

Some problems shown on graphing by taking points.

Shown the symmetry concept practically by papers and markers

Shown to draw graph up to third order equations by implementing the concept of intercept and symmetry

Handouts N/AN/A

N/A

Homework Some problems from Exercise-1.2 based on that conceptions

Some problems from Exercise-1.2 based on that conceptions

Some problems from Exercise-1.2 based on that conceptions

Evaluation Students done some problems based on the conceptions.

Students done some problems based on the conceptions.

Started my Tutorial class on every Wednesday to evaluate the students

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Pre-Calculus Lesson PlanWeek 3

1st class 2nd class 3rd class Objectives Calculate and interpret

the slope of a line,Graph lines given a point and the slope,Find the equation of a vertical line and horizontal line

To learn negative slope,

To find the line equation from intercept and slope,

To find the equation of parallel lines

Find equation of perpendicular lines

Class Outline Drawing graphs up to 3rd

order equation,Concept of slope,Some example problems on that concept,Derive the equation of a line given slope and one point,Shown how to find the slope of a vertical and horizontal line and work out some example problems

Recap of previous class on drawing graphs quickly by knowing the shapes up to 3 order equation.

Negative slope, Practically shown to form Negative slope,

Drawing graphs by knowing intercept and slope from equation,

Finding equations of parallel lines,

Difference between similar and congruent triangle,

Proof of parallel lines having same slope by similar triangle method

Recap of proof of parallel lines equation,

Recap of horizontal and vertical lines equation,

Concept of Perpendicular lines and its equation

Handouts None None Problem sheet on the concepts taught

Homework Some problems from Exercise-1.2 based on that conceptions

None Exercise 1.3 from Larson’s Precalculus book.

Evaluation Students done some problems based on the conceptions.

Students done some problems based on the conceptions.

Problems given to the students from Larson book, not been able to complete the pre-planned selected problems for evaluation because of lack of time.

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Evaluation Some Students worked out problems based on the conceptions correctly, however they have some confusion specially on parallel and perpendicular line equation

Evaluation is done by (2nd class of the week Tutorial Class) where the students solved some selected problems from Exercise 1.3. Most of them responded well.


Week 4

1st class 2nd class 3rd class Objectives To test the concept of the whole

chapter (Slope, straight line equation)To make students familiar with Application based problems,

To model a problem from data

Class postponed due to Strike

Class Outline Various problems on slope, vertical

line, horizontal line, slope-intercept form, slope- point form, parallel and perpendicular line and graphing them.

Some problems on straight lines based on Application.Some problems on linear curve fitting from given data

Handouts Some Vocabulary to familiar with none

Homework Some problems from Larson’s Precalculus Book

Some problems on application based problems

Evaluation Some Students worked out problems based on the conceptions correctly, however they have some confusion specially on parallel and perpendicular line equation

Evaluation is done by Wednesday Tutorial Class where the students solved some selected problems from Exercise 1.3. Most of them responded well.

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1st class 2nd class 3rd class

Objectives SWBAT form the sum, difference, product, and quotient of two functions.Discussing the Quiz-1 mistakes.

SWBAT understand what difference quotient of a function is and how it is related to calculus. SWBAT learn how apply the function’s problem in real life.

SWBAT identify the graph of a function.

Class Outline

First 25 minutes I discussed the mistakes which Ss did on the Quiz-1.Then I showed the formula Sum ,difference, product, and quotient for function and I taught how to solve The problems 62, and 70 ( Ex2.1 , Sullivan). Then I asked Ss to solve 64, 66, 68, 69, 71 and 72. Ss went through the problem individually and I was roaming to see Ss work.

.

Introduction –key vocabulary (difference quotient). I give an example and showed that graphically then I asked to solve 74, 76,78,80( Ex:2.1 Sullivan)……..Ss start to solve individually and answer was written on the board .Ss took 20 minutes to solve , then I taught Application problem from Blitzer book ( page 162 problem 99-102)

Introduction –key vocabulary (Graph of a function, Vertical-line test) and I taught how to work with the problem 10, 12 (Ex: 2.2 Sullivan). Then I asked to solve 11, 13, 14, 16, 18, 20 and 22. Ss solved individually and answer was written on the board.

Handouts Sullivan Ex:2.1 Work sheet -3 Ex: 2.2 ( Sullivan)

Homework 61,63,65,67,69 ( Ex:2.1 Sullivan) Solve worksheet -3. 9,15,17,19,21 ( Ex:2.2 Sullivan )

Evaluation Ss can easily understood formula and easily solve problems.

Ss can easily understood vocabulary and solve application problems.

Ss got fun when they were solving graph related problems.

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Objectives SWBAT determine where a Function is increasing and or decreasing and able to locate local Maximum and minimum.

SWBAT learn how apply the graph of the function.SWBAT learn how to find out Even Odd or neither even nor odd functions from graph .

One more lesson on Local Maximum and Minimum.

Class Outline

Introduction –key vocabulary (Increasing, decreasing, Local Max. and Local Min. ). Then I give an example to show how to find out Increasing , decreasing , Local Max and Local Min from a graph of a function . I asked to solve problems 11-20 ( Ex:2.3 Sullivan )

First 25 minutes I spend on Application problems from Blitzer book (Page 176, problem 83-90). Then Introduction –key vocabulary (Even and Odd functions).I showed problem no. 24. Asked to solve problem No. 22, 26, 28. Answer was written on the board.

Introduction –key vocabulary again (Local Maximum and Local Minimum) and I taught how to work with the problem 30 (Ex: 2.3 Sullivan). And few examples from me. Taught how to Locate the location of Max and Min and what is the difference of Max and Min values of a function s and their location .Then I asked to solve 29 and 32 ( Ex:2.3 )Ss solved individually and answer was written on the board.

Handouts Sullivan Ex:2.3 N/A N/A

Homework Revise 11-20 at home Ex: 2.3 ( problems 21, 23, 25, 27 from Sullivan Book )

Revise Ex:2.3

Evaluation Most of the student struggle with 15 and 16.

Ss can easily understood vocabulary and solve problems.

At first few students struggle then they got fun and said Max and Min is not difficult.


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Week 7

1st class 2nd class 3rd class Objectives To find the average rate of change

of function,

TO find the equation of a secant line.

Review of the Last class To graph the Functions listed in the Library of Functions;

Class Outline

Recap of even and odd functions and to relate them with symmetry,

Shown some numerical problems on finding even and odd function graphically and algebraically,

Secant line concept,

How to guess function from secant line,

Worked out a problem on Secant line.

Relation between even odd and symmetry and shown some problems on that.Shown some problems on average rate of change of Function and Slope of Secant Line

Shown how to draw square root function,Cube root function, Absolute value function, square function, Cube function, Reciprocal Function ,By using some of the properties such as even or odd property, intercept, increasing or decreasing or constant etc

Handouts NONE None None.

Homework Exercise 2.2 (11-27) Exercise 2.3 (11 – 44, 53 - 62)

Drawing the Parents Functions mentioned above with property.

Evaluation Get few problems done by students, students got confused on the y-intercept of secant line and y-intercept of function, i.e. they mixed up these two.

Students solved few problems from Exercise and rectified the previous difficulties.

Discussed on the Questions given in the CT on Wednesday Tutorial Class


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Week 8

1st class 2nd class 3rd class Objectives Revision for

Midterm. Midterm SWBAT derivative as a function.

Class Outline

Revised all concepts in Midterms .

Students took Midterm

I give the definition of derivative of the function W.R.T variable. Then I taught how work with this definition. Student worked with the problems 2,4,6,8,10,12 and match Answer with me .

Handouts A work sheet Question paper .

Ex:3.2 ( Thoman Calculus)

Homework Preparation for Midterm.

N/A Ex: 3.2 (1,3,5,7,9,11)

Evaluation Class went well. N/A Ss could easily understand and solve the problems.


1st class 2nd class 3rd class Objectives We could

not take Class for Strike

SWBAT understand The derivative as a function.

SWBAT understand One-sided Derivatives and Differentiability.

Class Outline

N/A I gave an example And solve problem 8 ( Ex 3.2 Thomas Book ) . Then I asked to solve from Ex:3.2 (10,12,14,16,18,20,25,26 Thomas Book)I was roaming the class and see their solution.

I taught how to solve problems 37 and 38 ( Ex:3.2 Thomas ) then student worked with the problems 39 and 40. Then solved 46 .I was observing Ss work.

Handouts N/A Ex:3.2 N/A

Homework N/A Ex:3.2(7,9,11,13,15,17,19,21,22,23,24) Ex: 3.2(39,40,43,44,45,47,48)

Evaluation N/A. Most of the students fells that problems are so calculation depended.

Ss could not easily understand “Differentiability”.

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Objectives 2nd lesson on Graph different functions which is related to Piecewise functions.

SWBT Linear functions and their properties.

SWBT understand the application related to the Ex: 2.5 and Ex: 3.1 .

Class Outline

Class was start with the problem no.29 ( Ex:2.4 Sullivan). Then I asked to solve 30,31,32 and 33. Ss worked with the problem. I checked each students answer when they were working.

I start the class with Concepts and Vocabulary. Then for skill building I solved 14 and 18 from Ex: 3.1 (Sullivan Book). Ss Worked with 16,20 , 22,24,28,32,33 from Ex: 3.1.Answer was written on the board.

In the class I solved one problem from Sullivan book ( Ex: 3.1 ,40 ) . Then I solved two problems from Blitzer book, Page 217 and 218.

Handouts N/A Ex: 3.1 Blitzer Page 217 , 218 and Work sheet -5

Homework Ex:2.4 (34,35,36,37,38) Ex:(21,23,25,27,29,31 ) Work Sheet-5

Evaluation Some of the students were struggling with graphing.

Ss easily solved the problems. Ss easily could understand the application problems and got fun.

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Week 11


Objectives 2nd lesson on (SWBT Understand) the application related to the Ex:2.5 and Ex: 3.1 .

SWBT draw and interpret scatter diagrams and Distinguish between linear and non linear relations .

SWBT understand the graphing utility to find the line of best fit and second lesson on previous lesson.

Class Outline

Class was start with the self created problems Then I asked to solve39 and 40 (Sullivan Book ). Ss worked with the problem. I checked each students answer when they were working.

I start the class with a example of scatter diagrams. Then for skill building I asked to solve 3,4,5,6,7,8. from Ex: 3.2 (Sullivan Book ). Ss Worked with 10 and 15 from Ex: 3.2.I checked each students answer and working process.

In the class I solved 18 (which was H.W.). Then I asked to solve 21 and 22.

Handouts N/A Ex: 3.2 N/A

Homework N/A Ex:3.2(16 18,) Preparation for 2nd Quiz.

Evaluation Ss easily could understand. Ss easily solved the problems. Ss easily could understand the application problems and got fun.

Pre-Calculus Class Lesson Plan

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Week 121st class 2nd class 3rd class

Objectives 2nd Quiz SWBT Building linear function from data and IDEA evaluation.

SWBT understand quadratic functions and their properties.

Class Outline

N/A At first I solved and explain problem no. 15 Ex:3.2 from Sullivan book .Then I asked to solve 16 . I checked each and every one answer. then student went to IDEA evaluation .

I introduced all key VocabularyFrom this concept (like Parabola , opens up , opens down , vertex , axis of symmetry etc )

Handouts N/A Ex: 3.2 Summary for quadratic functions.

Homework N/A Ex:3.2(18,) N/A

Evaluation Iron group did better than copper group.

Ss easily solved the problems. Ss easily could understand the vocabulary.

Pre-Calculus Class Lesson PlanWeek 13


Objectives Discuss with Quiz-2 problems and 2nd lesson on Quadratic functions.

SWBT Inequalities Involving Quadratic functions.

Second lesson on the Inequalities.

Class Outline

Class started with the Quiz-2 problems and then I solved problem no. 44 from Sullivan Ex. 3.3 . Then I asked Ss to solve 38,40,42,46,48,52 .Answer was written on the board .

I introduced key Vocabulary and give some example from Sullivan book. Then I made some problem and asked to solve. Then I select few problems from Ex 3.5 (Sullivan book), Ss solved the problems and Match answers.

I solved 32 for the students and asked to solve 26,28,30 from Ex:3.5 (Sullivan Book)


Homework Ex 3.3 ( 35,37,39,41,43,45,47,51,)

Ex:3.5(7,9,11,13,15,17,19,21,) Ex: 3.5 (25,27,29,31)

Evaluation Some of the student struggled with few problems.

Ss easily solved the problems. Some Ss struggled with the problem No. 30.

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Week 14


Objectives I’m going to start a new chapter. We will look at two general classes of function. One is polynomial another is rational function.

SWBT determine which functions are polynomial functions and graph few polynomial functions.

Third lesson on polynomial.

Class Outline

Introduced Key vocab. (What is polynomial function, degree of polynomial, power function, properties of power function , real zeros , multiplicity, turning points and end behavior, etc.)

I select few problems from Ex 4.1( Sullivan book ), Ss solved the problems and Match answer s.

I solved 38 and 50 for the students and asked to solve 40,42 and 44 , 46 ,48,52 and 56 from Ex:4.1 (Sullivan Book).


Homework

N/A Ex:4.1(,11,13,15,17,19,21,23,25,27,29,31 and 35)

Ex: 4.1(37,39,41,43,45,47,49,51,53 and 56)

Evaluation Some of the student struggled with few vocab.

Ss easily solved the problems. Some Ss struggled with the problem No. 52.

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9. ASSESSMENT METHODS

There will be a number of different ways that your learning will be assessed this year:

Participation (25%)

The participation mark is divided into three areas:

1. Attendance – 5% If you have no or one unexcused absence/late then you will receive the full 10% attendance mark. However, for two late attendances will be counted as one day absence. Three days of absence will result in the lose 60% of your marks. For example a student with 3 unexcused absences will receive an attendance mark of 2.

2. Lesson Contribution/Class Participation – 10%

The lesson contribution mark can be achieved by speaking at the board (50%), answering questions and other contributions (50%).

3. Assignments/ Homework – 10%

Quizzes (20%) There will be three or four quizzes in Fall – one for each Chapter that is covered in Sullivan Pre-calculus. Each quiz will be equal in weighting.

Mid-Term Exam (25%) The Mid-Term exam will test all of the content covered before Mid-Term date as provided with this syllabus.

Final Exam (30%) The Final Exam will test all of the content covered by the end of Fall semester.

10. KEY DATES & DEADLINES

Mid-Term Exam: Between 15th to 18th October.Final Exam: Between 9th to 13th December.

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11. PLAGIARISM & ACADEMIC INTEGRITY

All members of the AUW Community are bound by the Academic Honor Code published in the Academic Bulletin (http://www.auw.edu.bd/academics/course-bulletin/).

The integrity of students’ academic work is very important to AUW faculty. Universities are based upon the fundamental principle that the work presented truly belongs to the author, because the academic community revolves around ideas and creativity. Each person’s ideas are his or her contribution to the academic community. Therefore, taking another person’s ideas and representing them as one’s own is a serious form of dishonesty. Similarly, cheating (copying someone else’s work, asking for answers, sharing answers, etc.) and other forms of dishonesty (falsifying data, making up references, etc.) are also serious breaches of this honor code.

Plagiarism is intentionally or unintentionally taking credit for another’s words or ideas. You may not plagiarize in your academic work, and you must adhere to the following:

• When you use someone else’s words (whether they are from a distinguished author or a classmate’s paper), place the words you have copied in quotation marks and provide the appropriate citation of author and source. A good guideline to use to avoid plagiarism is to make sure quotes of three or more sequential words from someone else are put into quotation marks.

• If you paraphrase (reword) another person’s ideas, then you must also cite the source. Paraphrasing must involve changing the words and sentence structure of the original source.

• Cite materials you copy or paraphrase from the Internet, even if the author is not identified.

The various academic disciplines (humanities, social sciences, sciences) use slightly different formats for footnotes, endnotes, and bibliographies. Your professor for a particular class will tell you which format he or she wants you to use in that class.

Copying, asking for answers, sharing answers, and any other form of cheating (misrepresenting your own work and knowledge) on exams or quizzes are all forms of academic dishonesty.

Other Forms of Academic Dishonesty

1. Making up references, quoting wrong sources, etc. 2. Falsifying data. 3. Misrepresenting your situation to be excused from academic work. 4. Submitting the same paper in more than one class. 5. Informing a student in a later class about questions on tests or quizzes. 6. Misrepresenting your academic work or qualifications in any way.

12. STRATEGIES TO PREVENT PLAGIARIM& VIOLATIONS OF ACADEMIC INTEGRITY

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Students will not plagiarise –please see the Student Handbook.

13. CLASS BEHAVIOUR

o You are expected to be in class on time.o You should participate in class discussions and contribute to the class goal of learning

Pre-calculus.o Read your class notes over within 24 hours (or at least once before the next class).o Students will complete all home works and assignments given by the required deadlines. o Mobile phones and similar electronic devices such as MP3 players, laptops, and so on

should be switched off and put away at the beginning of class.o You will treat others in this class with respect.o Students are expected to check their email at least twice daily, preferably in the morning

and evening. Students are advised that a majority of faculty answer email within a 24 hour period during the week and a 48 hour period during weekends. Please be aware that students who do not check email regularly may miss important class announcements.

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Useful links from Khan Academy

Graphs: Graphs of equations in two variables

1) Two-variable linear equations intro

https://www.khanacademy.org/math/algebra/two-var-linear-equations/solutions-to-two-var-linear-equations/v/2-variable-linear-equations-graphs

Duration: 8 min 20 sec

2) Solutions to 2-variable equations

https://www.khanacademy.org/math/algebra/two-var-linear-equations/solutions-to-two-var-linear-equations/v/checking-ordered-pair-solutions-to-equations-1


3) Practice: Solutions to 2-variable equations

https://www.khanacademy.org/math/algebra/two-var-linear-equations/solutions-to-two-var-linear-equations/e/plugging_in_values

4) Completing solutions to 2-variable equations

https://www.khanacademy.org/math/algebra/two-var-linear-equations/solutions-to-two-var-linear-equations/v/graphing-solutions-to-2-variable-linear-equations-1


5) Lines, line segments, & rays

https://www.khanacademy.org/math/basic-geo/basic-geo-lines/lines-rays/v/lines-line-segments-and-rays


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6) Practice: Draw rays, lines, & line segments

https://www.khanacademy.org/math/basic-geo/basic-geo-lines/lines-rays/e/drawing-lines

Functions and their Graphs

1) What is a function?

https://www.khanacademy.org/math/algebra/algebra-functions/evaluating-functions/v/what-is-a-function


2) Recognizing functions from graph

https://www.khanacademy.org/math/algebra/algebra-functions/recognizing-functions-ddp/v/graphical-relations-and-functions


3) Testing if a relationship is a function

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-function-intro/v/testing-if-a-relationship-is-a-function


4) Practice: Recognize functions from graphs

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-function-intro/e/recog-func-2

5) Shifting & reflecting functions

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https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/shifting-and-reflecting-functions

Duration 6 min 39 sec

6) Intro to parabola transformations

https://www.khanacademy.org/math/algebra/quadratics/transforming-quadratic-functions/v/shifting-and-scaling-parabolas


7) Compressing functions

https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/compressing-functions-example


8) Practice: Transforming functions

https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/e/shifting_and_reflecting_functions

Linear and Quadratic Functions

1) Recognizing linear functions

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/linear-nonlinear-functions-tut/v/recognizing-linear-functions


2) Interpreting linear functions — Basic example

https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-heart-of-algebra/v/sat-math-h8-easier


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3) Linear function word problems — Harder example

https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-heart-of-algebra/v/sat-math-h3-harder


4) Graphing linear equations — Basic example



5) Graphing quadratics: standard form

https://www.khanacademy.org/math/algebra/quadratics/quad-standard-form-alg1/v/graphing-a-parabola-using-roots-and-vertex


6) Finding features of quadratic functions

https://www.khanacademy.org/math/algebra/quadratics/features-of-quadratic-functions/v/finding-features-of-quadratic-functions


7) Comparing features of quadratic functions

https://www.khanacademy.org/math/algebra/quadratics/features-of-quadratic-functions/v/comparing-features-of-quadratic-functions


8) Practice: Compare quadratic functions

https://www.khanacademy.org/math/algebra/quadratics/features-of-quadratic-functions/e/compare-properties-quadratic-functions

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Polynomial and Rational Functions

1) Intro to function symmetry

https://www.khanacademy.org/math/algebra2/polynomial-functions/introduction-to-symmetry-of-functions/v/recognizing-odd-and-even-functions

Duration of the video (minutes. seconds): 12.25

2) Intro to end behavior of polynomials

https://www.khanacademy.org/math/algebra2/polynomial-functions/polynomial-end-behavior/v/polynomial-end-behavior


3) Graphing rational functions according to asymptotes

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/graphs-of-rational-functions/v/finding-asymptotes-example


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