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  1. Preface
  2. 1 Prerequisites
    1. Introduction to Prerequisites
    2. 1.1 Real Numbers: Algebra Essentials
    3. 1.2 Exponents and Scientific Notation
    4. 1.3 Radicals and Rational Exponents
    5. 1.4 Polynomials
    6. 1.5 Factoring Polynomials
    7. 1.6 Rational Expressions
    8. Key Terms
    9. Key Equations
    10. Key Concepts
    11. Review Exercises
    12. Practice Test
  3. 2 Equations and Inequalities
    1. Introduction to Equations and Inequalities
    2. 2.1 The Rectangular Coordinate Systems and Graphs
    3. 2.2 Linear Equations in One Variable
    4. 2.3 Models and Applications
    5. 2.4 Complex Numbers
    6. 2.5 Quadratic Equations
    7. 2.6 Other Types of Equations
    8. 2.7 Linear Inequalities and Absolute Value Inequalities
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  4. 3 Functions
    1. Introduction to Functions
    2. 3.1 Functions and Function Notation
    3. 3.2 Domain and Range
    4. 3.3 Rates of Change and Behavior of Graphs
    5. 3.4 Composition of Functions
    6. 3.5 Transformation of Functions
    7. 3.6 Absolute Value Functions
    8. 3.7 Inverse Functions
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  5. 4 Linear Functions
    1. Introduction to Linear Functions
    2. 4.1 Linear Functions
    3. 4.2 Modeling with Linear Functions
    4. 4.3 Fitting Linear Models to Data
    5. Key Terms
    6. Key Concepts
    7. Review Exercises
    8. Practice Test
  6. 5 Polynomial and Rational Functions
    1. Introduction to Polynomial and Rational Functions
    2. 5.1 Quadratic Functions
    3. 5.2 Power Functions and Polynomial Functions
    4. 5.3 Graphs of Polynomial Functions
    5. 5.4 Dividing Polynomials
    6. 5.5 Zeros of Polynomial Functions
    7. 5.6 Rational Functions
    8. 5.7 Inverses and Radical Functions
    9. 5.8 Modeling Using Variation
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  7. 6 Exponential and Logarithmic Functions
    1. Introduction to Exponential and Logarithmic Functions
    2. 6.1 Exponential Functions
    3. 6.2 Graphs of Exponential Functions
    4. 6.3 Logarithmic Functions
    5. 6.4 Graphs of Logarithmic Functions
    6. 6.5 Logarithmic Properties
    7. 6.6 Exponential and Logarithmic Equations
    8. 6.7 Exponential and Logarithmic Models
    9. 6.8 Fitting Exponential Models to Data
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  8. 7 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 7.1 Systems of Linear Equations: Two Variables
    3. 7.2 Systems of Linear Equations: Three Variables
    4. 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 7.4 Partial Fractions
    6. 7.5 Matrices and Matrix Operations
    7. 7.6 Solving Systems with Gaussian Elimination
    8. 7.7 Solving Systems with Inverses
    9. 7.8 Solving Systems with Cramer's Rule
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  9. 8 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 8.1 The Ellipse
    3. 8.2 The Hyperbola
    4. 8.3 The Parabola
    5. 8.4 Rotation of Axes
    6. 8.5 Conic Sections in Polar Coordinates
    7. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Review Exercises
    11. Practice Test
  10. 9 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 9.1 Sequences and Their Notations
    3. 9.2 Arithmetic Sequences
    4. 9.3 Geometric Sequences
    5. 9.4 Series and Their Notations
    6. 9.5 Counting Principles
    7. 9.6 Binomial Theorem
    8. 9.7 Probability
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
  12. Index
A
absolute value function3.2 Domain and Range
Addition Principle9.5 Counting Principles
angle of rotation8.4 Rotation of Axes
annual percentage rate (APR)6.1 Exponential Functions
associative property of addition1.1 Real Numbers: Algebra Essentials
associative property of multiplication1.1 Real Numbers: Algebra Essentials
axes of symmetry8.2 The Hyperbola
C
center of a hyperbola8.2 The Hyperbola
center of an ellipse8.1 The Ellipse
central rectangle8.2 The Hyperbola
co-vertices8.1 The Ellipse
combining functions3.4 Composition of Functions
commutative property of addition1.1 Real Numbers: Algebra Essentials
commutative property of multiplication1.1 Real Numbers: Algebra Essentials
complement of an event 9.7 Probability
complex conjugate2.4 Complex Numbers
Complex Conjugate Theorem5.5 Zeros of Polynomial Functions
complex number2.4 Complex Numbers
complex plane2.4 Complex Numbers
composition of functions3.4 Composition of Functions
compound interest6.1 Exponential Functions
conjugate axis8.2 The Hyperbola
constant function3.2 Domain and Range
constant of variation5.8 Modeling Using Variation
coordinate plane8.3 The Parabola
correlation coefficient4.3 Fitting Linear Models to Data
D
decompose a composite function3.4 Composition of Functions
decreasing linear function4.1 Linear Functions
degenerate conic sections8.4 Rotation of Axes
Descartes’ Rule of Signs5.5 Zeros of Polynomial Functions
difference of squares1.4 Polynomials
domain of a composite function3.4 Composition of Functions
E
equation in quadratic form2.6 Other Types of Equations
experiment9.7 Probability
exponential function6.1 Exponential Functions
extraneous solutions2.6 Other Types of Equations
I
identity property of addition1.1 Real Numbers: Algebra Essentials
identity property of multiplication1.1 Real Numbers: Algebra Essentials
imaginary number2.4 Complex Numbers
increasing linear function4.1 Linear Functions
infinite geometric sequence9.4 Series and Their Notations
intersection9.7 Probability
inverse of a radical function5.7 Inverses and Radical Functions
inverse of a rational function5.7 Inverses and Radical Functions
inverse property of addition1.1 Real Numbers: Algebra Essentials
inverse property of multiplication1.1 Real Numbers: Algebra Essentials
inversely proportional5.8 Modeling Using Variation
P
partial fraction7.4 Partial Fractions
partial fraction decomposition7.4 Partial Fractions, 7.4 Partial Fractions
Pascal's Triangle9.6 Binomial Theorem
perfect square trinomial1.4 Polynomials
piecewise function3.2 Domain and Range
point-slope form4.1 Linear Functions
polynomial equation2.6 Other Types of Equations
probability9.7 Probability
probability model9.7 Probability
product of two matrices7.5 Matrices and Matrix Operations
properties of determinants7.8 Solving Systems with Cramer's Rule
R
reciprocal function5.6 Rational Functions
Restricting the domain3.7 Inverse Functions
S
sample space9.7 Probability
solving systems of linear equations7.1 Systems of Linear Equations: Two Variables
square root property2.5 Quadratic Equations
standard form of a quadratic function5.1 Quadratic Functions
system of three equations in three variables7.8 Solving Systems with Cramer's Rule
U
union of two events9.7 Probability
upper limit of summation9.4 Series and Their Notations
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