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College Algebra release 15.33
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FULL VERSION
Contents
- Rectangular Coordinate System
- Rectangular Coordinates of a Point
- The Distance Formula
- Circles
- The Midpoint Formula
- Functions and Graphs
- Basic Definitions and Notations
- Graphs of Functions
- Composite Functions
- Inverse Functions
- Transformations of Graphs
- Translating Graphs of Functions
- Stretching and Compressing Graphs of Functions
- Combining Transformations
- Graphic Solution of Equations
- Graphic Solution of Inequalities
- Linear and Absolute Value Functions
- Solving Linear Equations
- Solving Linear Inequalities
- Equations of Straight Lines
- Graphs and Graphic Solutions
- Graph of the Function y=ax + b
- Graph of the Function y=|ax+b|
- Graphic Solution of the Equation |ax + b| = c
- Graphic Solution of the Inequality |ax + b| <> c
- Slope of a Line
- Point-Slope Equation of a Line
- Slope-Intercept Equation of a Line
- Slopes for Parallel Lines
- Slopes for Perpendicular Lines
- Solving Equations Involving Absolute Values
- Solving Inequalities Involving Absolute Values
- Systems of Linear Inequalities
- Graphic Solution of a System of Two Linear Inequalities in Two Variables
- Graphic Solution of a System of Three Linear Inequalities
- Quadratic Functions
- Completing the Square
- Factoring Trinomials by Completing the Square
- Graphs of Quadratic Functions
- Maximum and Minimum Problems
- Solving Quadratic Equations
- Solving Quadratic Equations by Completing the Square
- Solving Quadratic Equations by General Formula
- The Sum and the Product of the Roots
- Graphic Solution of Quadratic Inequalities
- Polynomial and Rational Functions
- Operations with Polynomials
- Addition of Polynomials
- Subtraction of Polynomials
- Multiplication of Polynomials
- Division of Polynomials
- The Remainder Theorem
- The Factor Theorem
- Descartes' Rule of Signs
- Rational Zeros
- Asymptotes
- Vertical Asymptotes for the Graph of Rational Functions
- Horizontal Asymptotes for the Graph of Rational Functions
- Oblique Asymptotes for the Graph of Rational Functions
- Exponential and Logarithmic Functions
- Graphs of Functions
- Exponential Function
- Logarithmic Function
- Exponential and Logarithmic Functions
- Properties of Logarithms
- Solving Exponential and Logarithmic Equations
- Solving Exponential Equations
- Solving Logarithmic Equations
- Applications
- Compound Interest
- Growth and Decay
- Second Degree Equations
- The Parabola
- The Ellipse
- The Hyperbola
- Determinants and Cramer's Rule
- Determinants of Order 2
- Determinants of Order 3
- Definition and Properties of Determinants
- Minors and Cofactors
- The Expansion Theorem
- Systems of Two Linear Equations in Two Unknowns. Cramer's Rule
- Systems of Three Linear Equations in Three Unknowns. Cramer's Rule
- Matrices
- Basic Definitions
- Matrix Addition
- The Scalar Product
- Matrix Multiplication
- Inverses of Matrices
- Systems of Equations: Use of Matrix Inverses
- Complex Numbers
- Basic Definitions and Graphical Representation of Complex Numbers
- Operations with Complex Numbers
- Conjugate Complex Numbers
- Addition
- Subtraction
- Multiplication
- Division
- Complex Roots of a Quadratic Equation
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