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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 The Unit Circle: Sine and Cosine Functions
    1. Introduction to The Unit Circle: Sine and Cosine Functions
    2. 7.1 Angles
    3. 7.2 Right Triangle Trigonometry
    4. 7.3 Unit Circle
    5. 7.4 The Other Trigonometric Functions
    6. Key Terms
    7. Key Equations
    8. Key Concepts
    9. Review Exercises
    10. Practice Test
  9. 8 Periodic Functions
    1. Introduction to Periodic Functions
    2. 8.1 Graphs of the Sine and Cosine Functions
    3. 8.2 Graphs of the Other Trigonometric Functions
    4. 8.3 Inverse Trigonometric Functions
    5. Key Terms
    6. Key Equations
    7. Key Concepts
    8. Review Exercises
    9. Practice Test
  10. 9 Trigonometric Identities and Equations
    1. Introduction to Trigonometric Identities and Equations
    2. 9.1 Solving Trigonometric Equations with Identities
    3. 9.2 Sum and Difference Identities
    4. 9.3 Double-Angle, Half-Angle, and Reduction Formulas
    5. 9.4 Sum-to-Product and Product-to-Sum Formulas
    6. 9.5 Solving Trigonometric Equations
    7. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Review Exercises
    11. Practice Test
  11. 10 Further Applications of Trigonometry
    1. Introduction to Further Applications of Trigonometry
    2. 10.1 Non-right Triangles: Law of Sines
    3. 10.2 Non-right Triangles: Law of Cosines
    4. 10.3 Polar Coordinates
    5. 10.4 Polar Coordinates: Graphs
    6. 10.5 Polar Form of Complex Numbers
    7. 10.6 Parametric Equations
    8. 10.7 Parametric Equations: Graphs
    9. 10.8 Vectors
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  12. 11 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 11.1 Systems of Linear Equations: Two Variables
    3. 11.2 Systems of Linear Equations: Three Variables
    4. 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 11.4 Partial Fractions
    6. 11.5 Matrices and Matrix Operations
    7. 11.6 Solving Systems with Gaussian Elimination
    8. 11.7 Solving Systems with Inverses
    9. 11.8 Solving Systems with Cramer's Rule
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  13. 12 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 12.1 The Ellipse
    3. 12.2 The Hyperbola
    4. 12.3 The Parabola
    5. 12.4 Rotation of Axes
    6. 12.5 Conic Sections in Polar Coordinates
    7. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Review Exercises
    11. Practice Test
  14. 13 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 13.1 Sequences and Their Notations
    3. 13.2 Arithmetic Sequences
    4. 13.3 Geometric Sequences
    5. 13.4 Series and Their Notations
    6. 13.5 Counting Principles
    7. 13.6 Binomial Theorem
    8. 13.7 Probability
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  15. A | Proofs, Identities, and Toolkit Functions
  16. 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
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index
A
absolute value function3.2 Domain and Range
Addition Principle13.5 Counting Principles
angle of rotation12.4 Rotation of Axes
angular speed7.1 Angles, 7.1 Angles
annual percentage rate (APR)6.1 Exponential Functions
Archimedes’ spiral10.4 Polar Coordinates: Graphs
area of a sector7.1 Angles
associative property of addition1.1 Real Numbers: Algebra Essentials
associative property of multiplication1.1 Real Numbers: Algebra Essentials
axes of symmetry12.2 The Hyperbola
C
Cartesian equation10.3 Polar Coordinates
center of a hyperbola12.2 The Hyperbola
center of an ellipse12.1 The Ellipse
central rectangle12.2 The Hyperbola
circumference7.1 Angles
co-vertices12.1 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 13.7 Probability
complex conjugate2.4 Complex Numbers
Complex Conjugate Theorem5.5 Zeros of Polynomial Functions
composition of functions3.4 Composition of Functions
compound interest6.1 Exponential Functions
conjugate axis12.2 The Hyperbola
constant function3.2 Domain and Range
constant of variation5.8 Modeling Using Variation
coordinate plane12.3 The Parabola
correlation coefficient4.3 Fitting Linear Models to Data
coterminal angles7.1 Angles, 7.1 Angles
D
decompose a composite function3.4 Composition of Functions
decreasing linear function4.1 Linear Functions
degenerate conic sections12.4 Rotation of Axes
Descartes’ Rule of Signs5.5 Zeros of Polynomial Functions
difference of squares1.4 Polynomials
displacement7.1 Angles
domain of a composite function3.4 Composition of Functions
dot product10.8 Vectors
E
equation in quadratic form2.6 Other Types of Equations
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 sequence13.4 Series and Their Notations
initial side7.1 Angles
inner-loop limaçons10.4 Polar Coordinates: Graphs
intersection13.7 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
inverse tangent function8.3 Inverse Trigonometric Functions
inversely proportional5.8 Modeling Using Variation
L
least squares regression4.3 Fitting Linear Models to Data
linear speed7.1 Angles
lower limit of summation13.4 Series and Their Notations
P
parallelograms10.8 Vectors
partial fraction11.4 Partial Fractions
partial fraction decomposition11.4 Partial Fractions, 11.4 Partial Fractions
Pascal's Triangle13.6 Binomial Theorem
perfect square trinomial1.4 Polynomials
piecewise function3.2 Domain and Range
point-slope form4.1 Linear Functions
polar form of a complex number10.5 Polar Form of Complex Numbers
polynomial equation2.6 Other Types of Equations
position vector10.8 Vectors, 10.8 Vectors
positive angle7.1 Angles
probability13.7 Probability
probability model13.7 Probability
properties of determinants11.8 Solving Systems with Cramer's Rule
R
radian measure7.1 Angles
reciprocal function5.6 Rational Functions
Restricting the domain3.7 Inverse Functions
resultant10.8 Vectors
S
sample space13.7 Probability
SAS (side-angle-side) triangle10.2 Non-right Triangles: Law of Cosines
sector of a circle7.1 Angles
solving systems of linear equations11.1 Systems of Linear Equations: Two Variables
square root property2.5 Quadratic Equations
SSS (side-side-side) triangle10.2 Non-right Triangles: Law of Cosines
standard form of a quadratic function5.1 Quadratic Functions
sum and difference formulas for cosine9.2 Sum and Difference Identities
sum and difference formulas for sine9.2 Sum and Difference Identities
sum and difference formulas for tangent9.2 Sum and Difference Identities
system of three equations in three variables11.8 Solving Systems with Cramer's Rule
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