College Algebra (MATH 131 B)

Lecture Note at Union College

Instructor:   Dr. Seongchun (Michelle) Kwon
e-mail:   kwonseon at hotmail dot com

Most video lectures are taken from either ProfRobBob(R) or mathispower4u(J).
I thank to Mr.Tarrou and Prof. Sousa for their willingness to share their high quality lectures for this hybrid course.

( Partly based on the Powerpoint provided by Cengage Learning )
Video Resource
1.1. Graphs of Equations Plotting Points on the Coordinate Plane (J)
Graphing Equations By Plotting Points - Part 1 (J)
Graphing Equations By Plotting Points - Part 2 (J)
Graphing by Finding Intercepts (J)
Symmetry Introduction: x-axis, y-axis, the origin (J)
Ex: Determine Symmetry about the x-axis, y-axis, and the origin (J)
Ex: Write the Standard Form of a Circle From a Graph (J)
Ex 1: Find Standard Equation of a Circle Given the Endpoints of a Diameter(J)
Ex 2: Find Standard Equation of a Circle Given the Endpoints of a Diameter (J)
1.2. Linear Equations in One Variable Solving One Step Equations: The Basic (J)
Solving Two Step Equations: The Basics (J)
Solving One Step Equations Involving Fractions (J)
Solving Two Step Equations Involving Fractions (J)
Ex: Solving a Multi-Step Linear Equation in One Variable (J)
Solving Rational Equations (R): Watch up to 12 minutes
Solving Rational Equations (R): Watch up to 10:09 minutes
1.3. Modeling with Linear Equations Ex: Linear Equation Application (Cost of a Rental Car) (J)
Ex: Linear Equation Model for Submarine Depth (J)
Ex: Given a Linear Model, Interpret the Meaning of the Slope and Make Predictions (J)
Ex: Linear Equation Application (Write a Cost Equation) (J)
1.4. Quadratic Equations and Applications Factoring Quadratic Trinomial x^2+bx+c Polynomial (R)
Factoring Quadratic Trinomial ax^2+bx+c (R)
Factoring by Grouping (R)
Solving Quadratic Equations by Factoring (J)
Factoring Basic Trinomials with a = 1 (J)
Completing the Square to Solve Quadratic Equations (J)
The Quadratic Formula (J)
1.5. Complex Numbers Complex (imaginary) Numbers Part 1 (R)
1.6. Other Types of Equations Ex 1: Solve a Basic Radical Equation - Square Roots (J)
Equations with Radicals(R): You don't have to study cubed root one.
Solving Rational Equations(J)
Ex 2: Solving Absolute Value Equations(J)
1.7. Linear Inequalities in One Variable Solving One-Step Linear Inequalities in One Variable(J)
Solving Two-Step Linear Inequalities in One Variable(J)
Solving Linear Inequalities in One Variable(J): Watch up to 5:50
1.8. Other Types of Inequalities Solving Quadratic Inequalities(J)
Solving Polynomial Inequalities(R)
Solving Rational Inequalities(R)
2.1. Linear Equations in Two Variables (In-Class Lecture Version) Slope and Equations of Lines(R)
Equations of Lines and Graphing(R)
Equations of parallel and perpendicular lines(R)
2.2. Functions (In-Class Lecture Version) Function vs Relation(R)
Piecewise Functions(R)
Determining Domain of Functions(R)
Ex: Determine the Domain of a Rational Function(J)
Ex: Domain and Range of Square Root Functions(J)
Difference Quotient(R):
Part 1( up to 6:15): Geometric interpretation of the difference quotient
Part 2 (6:16 - 10:29) Example with a linear function
Part 3 ( 10:45 - end) Example with a quadratic equation : This is the most important example.
2.3. Analyzing Graphs of Functions
( Summary Version)
Visually identifying key characteristics of graphs(R)
Average Rate of Change(R)
Even Odd Functions & Symmetry(R)
2.4. A Library of Parent Functions
2.5. Transformations of Functions Transformation of Functions(R)
2.6. Combinations of Functions: Composite Functions Combining Functions Function Operations
Composition of Functions(R)
2.7. Inverse Functions Inverse Functions(J)
Inverse Functions(R)
3.1. Quadratic Functions and Models Graphing Quadratic Functions in General Form(J)
Ex1: Write a Quadratic Function in Standard Form to Graph(J)
Ex2: Write a Quadratic Function in Standard Form to Graph (a not 1)(J)
Graphing Quadratic Functions in Standard Form(J)
Ex: Quadratic Function Review(J)
Ex 1: Key Characteristics of the Graph of a Quadratic Function ( Opens Up)(J)
Ex 2: Key Characteristics of the Graph of a Quadratic Function ( Opens Down)(J)
Graphing Parabolas w/ vertex & intercepts(R)
3.2. Polynomial Functions of Higher Degree Polynomial Graphs Part 1(R)
Polynomial Graphs Part 2(R)
Intermediate Value Theorem(J)
3.3. Polynomial and Synthetic Division Long Division of Polynomials(R)
Synthetic Division & Remainder Theorem(R)
3.4. Zeros of Polynomial Functions Polynomial Function - Complex Factorization Theorem(J)
Ex 1: Find the Zeros of a Polynomial Function - Integer Zeros(J)
Finding polynomials using the Linear Factorization Theorem(R)
4.1. Rational Functions and Asymptotes Horizontal Asymptotes of rational equations(R)
Finding vertical asymptotes and holes of rational equations(R)
Graphing Rational Functions Part 1(R)
4.2. Graphs of Rational Functions Determining Vertical and Horizontal Asymptotes of Rational Functions(J): Watch up to 9:18
Determining Slant Asymptotes of Rational Functions(J)
5.1. Exponential Functions and Their Graphs Graphing Exponential Functions(R)
5.2. Logarithmic Functions and Their Graphs Logarithm Introduction(R)
Graphing Logarithms
5.3. Properties of Logarithms Change of Base Formula Logarithms(R)
Properties of Logarithms Part 1(R)
Properties of Logs Part 2(R)
5.4. Exponential and Logarithmic Equations Solving Equations with Logarithms Pt 1(R)
5.5.Exponential and Logarithmic Models (Optional)