MyLab Math for Trigsted College Algebra -- Access Card

College Algebra, by Kirk Trigsted, is the first text written from the ground up to take full advantage of the tools and functionality of MyMathLab. The author draws on his many years of teaching experience and MyMathLab usage to write and design an e-book that works with the way students think and behave online. Building on well-tested content, the intuitive approach keeps students motivated and engaged with timely hyperlinks to definitions and multimedia learning aids. In addition to creating a first rate text, Kirk has also scripted all of his own animations and videos so that all learning aids have a consistent approach and tone. By integrating technology with mathematics education, Kirk Trigsted’s College Algebra is the new online choice for students everywhere.

Table of Contents:

Chapter R. Review       

R.1 Real Numbers        

            1 Understanding the Real Number System

            2 Writing Sets Using Set-Builder Notation and Interval Notation

            3 Determining the Intersection and Union of Sets and Intervals

            4 Understanding Absolute Value

R.2 The Order of Operations and Algebraic Expressions

            1 Understanding the Properties of Real Numbers

            2 Using Exponential Notation

            3 Using the Order of Operations to Simplify Numeric and Algebraic Expressions

R.3 The Laws of Exponents; Radicals

            1 Simplifying Exponential Expressions Involving Integer Exponents

            2 Simplifying Radical Expressions

            3 Simplifying Exponential Expressions Involving Rational Exponents

R.4 Polynomials           

            1 Understanding the Definition of a Polynomial

            2 Adding and Subtracting Polynomials

            3 Multiplying Polynomials

            4 Dividing Polynomials Using Long Division

R.5 Factoring Polynomials

            1 Factoring a Greatest Common Factor

            2 Factoring by Grouping

            3 Factoring Trinomials with a Leading Coefficient Equal to One

            4 Factoring Trinomials with a Leading Coefficient Not Equal to One

            5 Factoring Using Special Factoring Formulas

R.6 Rational Expressions

            1 Simplifying Rational Expressions

            2 Multiplying and Dividing Rational Expressions

            3 Adding and Subtracting Rational Expressions

            4 Simplifying Complex Rational Expressions

Chapter 1. Equations, Inequalities, and Applications

1.1 Linear Equations     

            1 Recognizing Linear Equations

            2 Solving Linear Equations with Integer Coefficients

            3 Solving Linear Equations Involving Factions

            4 Solving Linear Equations Involving Decimals

            5 Solving Equations That Lead to linear Equations

1.2 Applications if Linear Equations

            1 Converting Verbal Statements into Mathematical Statements

            2 Solving Applications Involving Unknown Numeric Quantities

            3 Solving Applications Involving Decimal Equations (Money, Mixture, Interest)

            4 Solving Applied Problems Involving Distance, Rate, and Time

            5 Solving Applied Working Together Problems

1.3 Complex Numbers  

            1 Simplifying Powers of i

            2 Adding and Subtracting Complex Numbers

            3 Multiplying Complex Numbers

            4 Finding the Quotient of Complex Numbers

            5 Simplifying Radicals with negative Radicands

1.4 Quadratic Equations           

            1 Solving Quadratic Equations by Factoring and the Zero Product Property

            2 Solving Quadratic Equations Using the Square Root Property

            3 Solving Quadratic Equations by Completing the Square

            4 Solving Quadratic Equations Using the Quadratic Formula

            5 Using the Discriminant to Determine the Type of Solutions of a Quadratic Equation

1.5 Applications of Quadratic Equations

            1 Solving Applications Involving Unknown Numeric Quantities

            2 Using the Projectile Motion Model

            3 Solving Geometric Applications

            4 Solving Applications Involving Distance, Rate, and Time

            5 Solving Working Together Applications

1.6 Other Types if Equations

            1 Solving Higher-Order Polynomial Equations

            2 Solving Equations That Are Quadratic in Form ("Disguised Quadratics")

            3 Solving Equations Involving Radicals

1.7 Linear Inequalities   

            1 Solving Linear Inequalities

            2 Solving Three-Part Inequalities

            3 Solving Compound Inequalities

            4 Solving Linear Inequality Word Problems

1.8 Absolute Value Equations and Inequalities

            1 Solving an Absolute Value Equation

            2 Solving an Absolute Value "Less Than" Inequality

            3 Solving an Absolute Value "Greater Than" Inequality

1.9 Polynomial and Rational Inequalities

            1 Solving Polynomial Inequalities

            2 Solving Rational Inequalities

Chapter 2. The Rectangular Coordinate System, Lines, and Circles

2.1 The Rectangular Coordinate System

            1 Plotting Ordered Pairs

            2 Graphing Equations by Plotting Points

            3 Finding the Midpoint of a Line Segment Using the Midpoint Formula

            4 Finding the Distance between Two Points Using the Distance Formula

2.2 Circles        

            1 Writing the Standard Form of an Equation of a Circle

            2 Sketching the Graph of a Circle

            3 Converting the General Form of a Circle into Standard Form

2.3 Lines          

            1 Determining the Slope of a Line

            2 Sketching a Line Given a Point and the Slope

            3 Finding the Equation of a Line Using the Point-Slope Form

            4 Finding the Equation of a Line Using the Slope-Intercept Form

            5 Writing the Equation of a Line in Standard Form

            6 Finding the Slope and the y-Intercept of a Line in Standard Form

            7 Sketching Lines by Plotting Intercepts

            8 Finding the Equation of a Horizontal Line and a Vertical Line

2.4 Parallel and Perpendicular Lines

            1 Understanding the Definition of Parallel Lines

            2 Understanding the Definition of Perpendicular Lines

            3 Determining Whether Two Lines Are Parallel, Perpendicular, or Neither

            4 Finding the Equations of Parallel and Perpendicular Lines

            5 Solving a Geometric Application of Parallel and Perpendicular Lines

Chapter 3. Functions   

3.1 Relations and Functions

            1 Understanding the Definitions of Relations and Functions

            2 Determining Whether Equations Represent Functions

            3 Using Function Notation; Evaluating Functions

            4 Using the Vertical Line Test

            5 Determining the Domain of a Function Given the Equation

3.2 Properties of a Function's Graph

            1 Determining the Intercepts of a Function

            2 Determining the Domain and Range of a Function from Its Graph

            3 Determining Whether a Function Is Increasing, Decreasing, or Constant

            4 Determining Relative Maximum and Relative Minimum Values of a Function

            5 Determining Whether a Function Is Even, Odd, or Neither

            6 Determining Information about a Function from a Graph

3.3 Graphs of Basic Functions; Piecewise Functions

            1 Sketching the Graphs of the Basic Functions

            2 Analyzing Piecewise-Defined Functions

            3 Solving Applications of Piecewise-Defined Functions

3.4 Transformations of Functions

            1 Using Vertical Shifts to Graph Functions

            2 Using Horizontal Shifts to Graph Functions

            3 Using Reflections to Graph Functions

            4 Using Vertical Stretches and Compressions to Graph Functions

            5 Using Horizontal Stretches and Compressions to Graph Functions

            6 Using Combinations of Transformations to Graph Functions

3.5 The Algebra of Functions; Composite Functions

            1 Evaluating a Combined Function

            2 Finding the Intersection of Intervals

            3 Finding Combined Functions and Their Domains

            4 Forming and Evaluating Composite Functions

            5 Determining the Domain of Composite Functions

3.6 One-to-One Functions; Inverse Functions

            1 Understanding the Definition of a One-to-One Function

            2 Determining Whether a Function is One-to-One Using the Horizontal Line Test

            3 Understanding and Verifying Inverse Functions

            4 Sketching the Graphs of Inverse Functions

            5 Finding the Inverse of a One-to-One Function

Chapter 4. Polynomial and Rational Functions

4.1 Quadratic Functions

            1 Understanding the Definition of a Quadratic Function and Its Graph

            2 Graphing Quadratic Functions Written in Standard Form

            3 Graphing Quadratic Functions by Completing the Square

            4 Graphing Quadratic Functions Using the Vertex Formula

            5 Determining the Equation of a Quadratic Function Given Its Graph

4.2 Applications and Modeling of Quadratic Functions

            1 Maximizing Projectile Motion Functions

            2 Maximizing Functions in Economics

            3 Maximizing Area Functions

4.3 The Graphs of Polynomial Functions

            1 Understanding the Definition of a Polynomial Function

            2 Sketching the Graphs of Power Functions

            3 Determining the End Behavior of Polynomial Functions

            4 Determining the Intercepts of a Polynomial Function

            5 Determining the Real Zeros of Polynomial Functions and Their Multiplicities

            6 Sketching the Graph of a Polynomial Function

            7 Determining a Possible Equation of a Polynomial Function Given Its Graph

4.4 Synthetic Division; The Remainder and Factor Theorems

            1 Using the Division Algorithm

            2 Using Synthetic Division

            3 Using the Remainder Theorem

            4 Using the Factor Theorem

            5 Sketching the Graph of a Polynomial Function

4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra

            1 Using the Rational Zeros Theorem

            2 Finding the Zeros of a Polynomial Function

            3 Solving Polynomial Equations

            4 Using the Complex Conjugate Pairs Theorem

            5 Using the Intermediate Value Theorem

            6 Sketching the Graphs Polynomial Functions

4.6 Rational Functions and Their Graphs

            1 Finding the Domain and Intercepts of Rational Functions

            2 Identifying Vertical Asymptotes

            3 Identifying Horizontal Asymptotes

            4 Using Transformations To Sketch the Graphs of Rational Functions

            5 Sketching Rational Functions Having Removable Discontinuities

            6 Identifying Slant Asymptotes

            7 Sketching Rational Functions

Chapter 5. Exponential and Logarithmic Functions and Equations

5.1 Exponential Functions

            1 Understanding the Characteristics of Exponential Functions

            2 Sketching the Graphs of Exponential Functions Using Transformations

            3 Solving Exponential Equations by Relating the Bases

            4 Solving Applications of Exponential Functions

5.2 The Natural Exponential Functions

            1 Understanding the Characteristics of the Natural Exponential Function

            2 Sketching the Graphs of Natural Exponential Functions Using Transformations

            3 Solving Natural Exponential Equations by Relating the Bases

            4 Solving Applications of the Natural Exponential Function

5.3 Logarithmic Functions

            1 Understanding the Definition of a Logarithmic Function

            2 Evaluating Logarithmic Expressions

            3 Understanding the Properties of Logarithms

            4 Using the Common and Natural Logarithms

            5 Understanding the Characteristics of a Logarithmic Function

            6 Sketching the Graphs of Logarithmic Functions Using Transformations

            7 Finding the Domain of Logarithmic Functions

5.4 Properties of Logarithms

            1 Using the Product Rule, Quotient Rule, and Power Rule for Logarithms

            2 Expanding and Condensing Logarithmic Expressions

            3 Solving Logarithmic Equations Using the Logarithm Property of Equality

            4 Using the Change of Base Formula

5.5 Exponential and Logarithmic Equations

            1 Solving Exponential Equations

            2 Solving Logarithmic Equations

5.6 Applications of Exponential and Logarithmic Functions

            1 Solving Compound Interest Applications

            2 Exponential Growth and Decay

            3 Solving Logistic Growth Applications

            4 Using Newton's Law of Cooling

Chapter 6. Conic Sections

6.1 The Parabola          

            1 Determining the Equation of a Parabola with a Vertical Axis of Symmetry

            2 Determining the Equation of a Parabola with a Horizontal Axis of Symmetry

            3 Determining the Equation of a Parabola Given Information About the Graph

            4 Completing the Square to Find the Equation of a Parabola in Standard Form

            5 Solving Applied Problems Involving Parabolas

6.2 The Ellipse 

            1 Sketching the Graph of an Ellipses

            2 Determining the Equation of an Ellipse Given Information About the Graph

            3 Completing the Square to Find the Equation of an Ellipse in Standard Form

            4 Solving Applied Problems Involving Ellipses

6.3 The Hyperbola        

            1 Sketching the Graph of a Hyperbola

            2 Determining the Equation of a Hyperbola in Standard Form

            3 Completing the Square to Find the Equation of a Hyperbola in Standard Form

Chapter 7. Systems of Equations and Matrices

7.1 Systems of Linear Equations in Two Variables

            1 Verifying Solutions to Linear Systems in Two Variables

            2 Solving a System of Linear Equations Using the Substitution Method

            3 Solving a System of Linear Equations Using the Elimination Method

            4 Solving Applied Problems Using a System of Linear Equations

7.2 Systems of Linear Equations in Three Variables

            1 Verifying the Solution of a System of Three Linear Equations

            2 Solving a System of Linear Equations Using Gaussian Elimination

            3 Using an Augmented Matrix to Solve a System of Linear Equations

            4 Applications of Systems of Linear Equations Involving Three Variables

7.3 Inconsistent and Dependent Linear Systems in Three Variables

            1 Solving Linear Systems Having No Solutions

            2 Solving Linear Systems Having Infinitely Many Solutions

            3 Solving Linear Systems Having Fewer Equations Than Variables

7.4 Matrix Operations   

            1 Understanding the Definition of a Matrix

            2 Adding and Subtracting Matrices

            3 Scalar Multiplication of Matrices

            4 Multiplying Matrices

            5 Applications of Matrix Multiplication

7.5 Inverses of Matrices and Matrix Equations

            1 Understanding the Definition of an Inverse Matrix

            2 Finding the Inverse of a 2 x 2 Matrix

            3 Finding the Inverse of any Square Matrix

            4 Solving Systems of Equations using an Inverse Matrix

7.6 Determinants and Cramer's Rule

            1 Using Cramer's Rule to Solve Linear Systems in Two Variables

            2 Calculating the Determinant of an n x n Matrix by Expansion of Minors

            3 Using Cramer's Rule to Solve Linear Systems in n Variables

Chapter 8. Sequences and Series

8.1 Introduction to Sequences and Series

            1 Writing the terms of a sequence

            2 Writing the terms of a recursive sequence

            3 Writing the general term for a given sequence

            4 Computing partial sums of a series

            5 Writing a series using summation notation

8.2 Arithmetic Sequences and Series

            1 Determining if a sequence or series is arithmetic

            2 Writing the general term of an arithmetic sequence

            3 Computing the partial sums of an arithmetic series

8.3 Geometric Sequences and Series

            1 Determining if a sequence or series is geometric

            2 Writing the general term of a geometric sequence

            3 Computing partial sums of a geometric sequence

            4 Computing the sum of a convergent infinite geometric series

8.4 Binomial Theorem   

            1 Expanding binomials raised to a power by using Pascal's Triangle

            2 Computing binomial coefficients

            3 Expanding binomials raised to a power by using the Binomial Theorem

            4 Find the nth term of a binomial expansion

8.5 Mathematical Induction

             1 Writing Mathematical Statements

             2 Using the Principle of Mathematical Induction to Prove Statements