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Table of contents
  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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    9. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Concepts
    6. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    7. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    6. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Trigonometric Identities and Equations
    1. Introduction to Trigonometric Identities and Equations
    2. 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
    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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    8. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    8. Exercises
      1. Review Exercises
      2. 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. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. 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 function 3.2 Domain and Range
Addition Principle 13.5 Counting Principles
angle 7.1 Angles
angle of depression 7.2 Right Triangle Trigonometry
angle of rotation 12.4 Rotation of Axes
angular speed 7.1 Angles, 7.1 Angles
annual percentage rate (APR) 6.1 Exponential Functions
Archimedes’ spiral 10.4 Polar Coordinates: Graphs
area of a sector 7.1 Angles
arrow notation 5.6 Rational Functions
associative property of addition 1.1 Real Numbers: Algebra Essentials
associative property of multiplication 1.1 Real Numbers: Algebra Essentials
asymptotes 12.2 The Hyperbola
axes of symmetry 12.2 The Hyperbola
C
Cartesian equation 10.3 Polar Coordinates
center of a hyperbola 12.2 The Hyperbola
center of an ellipse 12.1 The Ellipse
central rectangle 12.2 The Hyperbola
circumference 7.1 Angles
co-vertex 12.1 The Ellipse
co-vertices 12.1 The Ellipse
combining functions 3.4 Composition of Functions
common logarithm 6.3 Logarithmic Functions
commutative property of addition 1.1 Real Numbers: Algebra Essentials
commutative property of multiplication 1.1 Real Numbers: Algebra Essentials
complement of an event 13.7 Probability
complex conjugate 2.4 Complex Numbers
Complex Conjugate Theorem 5.5 Zeros of Polynomial Functions
composite function 3.4 Composition of Functions
composition of functions 3.4 Composition of Functions
compound interest 6.1 Exponential Functions
conic section 12.4 Rotation of Axes
conic sections 10.6 Parametric Equations
conjugate axis 12.2 The Hyperbola
constant function 3.2 Domain and Range
coordinate plane 12.3 The Parabola
correlation coefficient 4.3 Fitting Linear Models to Data
coterminal angles 7.1 Angles, 7.1 Angles
curvilinear path 10.6 Parametric Equations
D
decompose a composite function 3.4 Composition of Functions
decomposition 11.4 Partial Fractions
decreasing linear function 4.1 Linear Functions
degenerate conic sections 12.4 Rotation of Axes
Descartes’ Rule of Signs 5.5 Zeros of Polynomial Functions
difference of squares 1.4 Polynomials
dimpled limaçons 10.4 Polar Coordinates: Graphs
displacement 7.1 Angles
distributive property 1.1 Real Numbers: Algebra Essentials
domain of a composite function 3.4 Composition of Functions
dot product 10.8 Vectors
E
equation in quadratic form 2.6 Other Types of Equations
experiment 13.7 Probability
exponential function 6.1 Exponential Functions
extraneous solutions 2.6 Other Types of Equations
I
identity property of addition 1.1 Real Numbers: Algebra Essentials
identity property of multiplication 1.1 Real Numbers: Algebra Essentials
imaginary number 2.4 Complex Numbers
inconsistent equation 2.2 Linear Equations in One Variable
increasing linear function 4.1 Linear Functions
index of summation 13.4 Series and Their Notations
infinite geometric sequence 13.4 Series and Their Notations
initial point 10.8 Vectors, 10.8 Vectors
initial side 7.1 Angles
inner-loop limaçons 10.4 Polar Coordinates: Graphs
intersection 13.7 Probability
inverse cosine function 8.3 Inverse Trigonometric Functions
inverse of a radical function 5.7 Inverses and Radical Functions
inverse of a rational function 5.7 Inverses and Radical Functions
inverse property of addition 1.1 Real Numbers: Algebra Essentials
inverse property of multiplication 1.1 Real Numbers: Algebra Essentials
inverse sine function 8.3 Inverse Trigonometric Functions
inverse tangent function 8.3 Inverse Trigonometric Functions
inverse variation 5.8 Modeling Using Variation
inverse variations 5.8 Modeling Using Variation
inversely proportional 5.8 Modeling Using Variation
invertible functions 5.7 Inverses and Radical Functions
L
least squares regression 4.3 Fitting Linear Models to Data
linear relationship 4.3 Fitting Linear Models to Data
linear speed 7.1 Angles
long division 5.4 Dividing Polynomials
lower limit of summation 13.4 Series and Their Notations
P
parallelograms 10.8 Vectors
partial fraction 11.4 Partial Fractions
partial fraction decomposition 11.4 Partial Fractions, 11.4 Partial Fractions
Pascal's Triangle 13.6 Binomial Theorem
perfect square trinomial 1.4 Polynomials
piecewise function 3.2 Domain and Range
point-slope form 4.1 Linear Functions
polar form of a complex number 10.5 Polar Form of Complex Numbers
polynomial equation 2.6 Other Types of Equations
position vector 10.8 Vectors, 10.8 Vectors
positive angle 7.1 Angles
probability 13.7 Probability
probability model 13.7 Probability
product of two matrices 11.5 Matrices and Matrix Operations
properties of determinants 11.8 Solving Systems with Cramer's Rule
Pythagorean identity 9.2 Sum and Difference Identities
R
radian measure 7.1 Angles
radical equation 2.6 Other Types of Equations
reciprocal function 5.6 Rational Functions
Restricting the domain 3.7 Inverse Functions
resultant 10.8 Vectors
S
sample space 13.7 Probability
SAS (side-angle-side) triangle 10.2 Non-right Triangles: Law of Cosines
sector of a circle 7.1 Angles
solving systems of linear equations 11.1 Systems of Linear Equations: Two Variables
square root property 2.5 Quadratic Equations
SSS (side-side-side) triangle 10.2 Non-right Triangles: Law of Cosines
standard form of a quadratic function 5.1 Quadratic Functions
standard position 7.1 Angles, 7.1 Angles, 10.8 Vectors
sum and difference formulas for cosine 9.2 Sum and Difference Identities
sum and difference formulas for sine 9.2 Sum and Difference Identities
sum and difference formulas for tangent 9.2 Sum and Difference Identities
summation notation 13.4 Series and Their Notations
system of three equations in three variables 11.8 Solving Systems with Cramer's Rule
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