Instructor: Dr. Seongchun (Michelle) Kwon
e-mail: kwonseon at hotmail dot com
PowerPoint ( 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 Corrected.mov(R) 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) |