College Algebra

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College Algebra release 25.63

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
- Graphic Solution of Equations
- Graphic Solution of Inequalities
Linear and Absolute Value Functions
- Linear Equations and Inequalities in One Variable
  - Solving Linear Equations
  - Solving Linear Inequalities
  - Solving Equations Involving Absolute Values
  - Solving Inequalities Involving Absolute Values
- 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
- Equations of Straight Lines
  - Slope of a Line
  - Slope-Intercept Equation of a Line
  - Point-Slope Equation of a Line
  - Slopes for Parallel Lines
  - Slopes for Perpendicular Lines
Systems of Linear Equations and Inequalities
- Systems of Two Linear Equations in Two Variables
  - Basic Concepts
  - Solutions Using Graphing
  - Solutions Using Substitution
  - Solutions Using Elimination
- Linear Inequalities in Two Variables
- Systems of Linear Inequalities in Two Variables
Polynomial and Rational Functions
- Division of Polynomials
- Roots of Polynomial Equations
  - The Factor Theorem
  - Rational Zeros
  - The Remainder Theorem
  - Descartes' Rule of Signs
- Graphing Rational Functions
  - Vertical Asymptotes for the Graph of Rational Functions
  - Horizontal Asymptotes for the Graph of Rational Functions
  - Oblique Asymptotes for the Graph of Rational Functions
Complex Numbers
- Basic Definitions and Graphical Representation of Complex Numbers
- Operations with Complex Numbers
  - Conjugate Complex Numbers
  - Addition
  - Subtraction
  - Multiplication
  - Division
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
  - Complex Roots of a Quadratic Equation
  - The Sum and the Product of the Roots
- Graphic Solution of Quadratic Inequalities
Conic Sections
- The Parabola
- The Ellipse
- The Hyperbola
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
  - Exponential Growth or Decay
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
- The Scalar Product
- Matrix Addition
- Matrix Multiplication
- Inverses of Matrices
- Systems of Equations: Use of Matrix Inverses
Sequences and Series
- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Infinite Geometric Series
Miscellaneous
- Binomial Theorem
  - Factorial Notation
  - Binomial Expansions
  - Pascal's Triangle
- Counting Principles
  - Permutations
    - Permutations of n Elements
    - Permutations of n Elements Taken r at a Time
    - Distinguishable Permutations
  - Combinations
  - Fundamental Counting Principles