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Table of contents
  1. Preface
  2. 1 Functions
    1. Introduction to Functions
    2. 1.1 Functions and Function Notation
    3. 1.2 Domain and Range
    4. 1.3 Rates of Change and Behavior of Graphs
    5. 1.4 Composition of Functions
    6. 1.5 Transformation of Functions
    7. 1.6 Absolute Value Functions
    8. 1.7 Inverse Functions
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Linear Functions
    1. Introduction to Linear Functions
    2. 2.1 Linear Functions
    3. 2.2 Graphs of Linear Functions
    4. 2.3 Modeling with Linear Functions
    5. 2.4 Fitting Linear Models to Data
    6. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Polynomial and Rational Functions
    1. Introduction to Polynomial and Rational Functions
    2. 3.1 Complex Numbers
    3. 3.2 Quadratic Functions
    4. 3.3 Power Functions and Polynomial Functions
    5. 3.4 Graphs of Polynomial Functions
    6. 3.5 Dividing Polynomials
    7. 3.6 Zeros of Polynomial Functions
    8. 3.7 Rational Functions
    9. 3.8 Inverses and Radical Functions
    10. 3.9 Modeling Using Variation
    11. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Exponential and Logarithmic Functions
    1. Introduction to Exponential and Logarithmic Functions
    2. 4.1 Exponential Functions
    3. 4.2 Graphs of Exponential Functions
    4. 4.3 Logarithmic Functions
    5. 4.4 Graphs of Logarithmic Functions
    6. 4.5 Logarithmic Properties
    7. 4.6 Exponential and Logarithmic Equations
    8. 4.7 Exponential and Logarithmic Models
    9. 4.8 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
  6. 5 Trigonometric Functions
    1. Introduction to Trigonometric Functions
    2. 5.1 Angles
    3. 5.2 Unit Circle: Sine and Cosine Functions
    4. 5.3 The Other Trigonometric Functions
    5. 5.4 Right Triangle Trigonometry
    6. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Periodic Functions
    1. Introduction to Periodic Functions
    2. 6.1 Graphs of the Sine and Cosine Functions
    3. 6.2 Graphs of the Other Trigonometric Functions
    4. 6.3 Inverse Trigonometric Functions
    5. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    6. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Trigonometric Identities and Equations
    1. Introduction to Trigonometric Identities and Equations
    2. 7.1 Solving Trigonometric Equations with Identities
    3. 7.2 Sum and Difference Identities
    4. 7.3 Double-Angle, Half-Angle, and Reduction Formulas
    5. 7.4 Sum-to-Product and Product-to-Sum Formulas
    6. 7.5 Solving Trigonometric Equations
    7. 7.6 Modeling with Trigonometric Functions
    8. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Further Applications of Trigonometry
    1. Introduction to Further Applications of Trigonometry
    2. 8.1 Non-right Triangles: Law of Sines
    3. 8.2 Non-right Triangles: Law of Cosines
    4. 8.3 Polar Coordinates
    5. 8.4 Polar Coordinates: Graphs
    6. 8.5 Polar Form of Complex Numbers
    7. 8.6 Parametric Equations
    8. 8.7 Parametric Equations: Graphs
    9. 8.8 Vectors
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 9.1 Systems of Linear Equations: Two Variables
    3. 9.2 Systems of Linear Equations: Three Variables
    4. 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 9.4 Partial Fractions
    6. 9.5 Matrices and Matrix Operations
    7. 9.6 Solving Systems with Gaussian Elimination
    8. 9.7 Solving Systems with Inverses
    9. 9.8 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
  11. 10 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 10.1 The Ellipse
    3. 10.2 The Hyperbola
    4. 10.3 The Parabola
    5. 10.4 Rotation of Axes
    6. 10.5 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
  12. 11 Sequences, Probability and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 11.1 Sequences and Their Notations
    3. 11.2 Arithmetic Sequences
    4. 11.3 Geometric Sequences
    5. 11.4 Series and Their Notations
    6. 11.5 Counting Principles
    7. 11.6 Binomial Theorem
    8. 11.7 Probability
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Introduction to Calculus
    1. Introduction to Calculus
    2. 12.1 Finding Limits: Numerical and Graphical Approaches
    3. 12.2 Finding Limits: Properties of Limits
    4. 12.3 Continuity
    5. 12.4 Derivatives
    6. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  14. A | Basic Functions and Identities
  15. 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
  16. Index
A
AAS (angle-angle-side) 8.1 Non-right Triangles: Law of Sines
absolute value equation 1.6 Absolute Value Functions
absolute value inequality 1.6 Absolute Value Functions
Addition Principle 11.5 Counting Principles
angle of depression 5.4 Right Triangle Trigonometry
angle of rotation 10.4 Rotation of Axes
angular speed 5.1 Angles
annual percentage rate (APR) 4.1 Exponential Functions
Archimedes’ spiral 8.4 Polar Coordinates: Graphs
area of a sector 5.1 Angles, 5.1 Angles
arrow notation 3.7 Rational Functions
asymptotes 10.2 The Hyperbola
axes of symmetry 10.2 The Hyperbola
C
Cartesian equation 8.3 Polar Coordinates
center of a hyperbola 10.2 The Hyperbola
center of an ellipse 10.1 The Ellipse
central rectangle 10.2 The Hyperbola
circumference 5.1 Angles
co-vertex 10.1 The Ellipse
co-vertices 10.1 The Ellipse
combining functions 1.4 Composition of Functions
common logarithm 4.3 Logarithmic Functions
complement of an event 11.7 Probability
Complex Conjugate Theorem 3.6 Zeros of Polynomial Functions
composite function 1.4 Composition of Functions
composition of functions 1.4 Composition of Functions
compound interest 4.1 Exponential Functions
conic section 10.4 Rotation of Axes
conic sections 8.6 Parametric Equations
conjugate axis 10.2 The Hyperbola
constant of variation 3.9 Modeling Using Variation
constant rate of change 2.3 Modeling with Linear Functions
coordinate plane 10.3 The Parabola
correlation coefficient 2.4 Fitting Linear Models to Data
coterminal angles 5.1 Angles, 5.1 Angles, 5.1 Angles
curvilinear path 8.6 Parametric Equations
D
decompose a composite function 1.4 Composition of Functions
decomposition 9.4 Partial Fractions
decreasing linear function 2.1 Linear Functions
degenerate conic sections 10.4 Rotation of Axes
Descartes’ Rule of Signs 3.6 Zeros of Polynomial Functions
difference quotient 12.4 Derivatives
differentiable 12.4 Derivatives
dimpled limaçons 8.4 Polar Coordinates: Graphs
direct variation 3.9 Modeling Using Variation
discontinuous 12.3 Continuity
discontinuous function 12.3 Continuity
displacement 5.1 Angles
domain of a composite function 1.4 Composition of Functions
dot product 8.8 Vectors
E
experiment 11.7 Probability
exponential function 4.1 Exponential Functions
I
imaginary number 3.1 Complex Numbers
increasing linear function 2.1 Linear Functions
index of summation 11.4 Series and Their Notations
infinite geometric sequence 11.4 Series and Their Notations
initial point 8.8 Vectors, 8.8 Vectors
initial side 5.1 Angles
inner-loop limaçons 8.4 Polar Coordinates: Graphs
instantaneous rate of change 12.4 Derivatives
instantaneous velocity 12.4 Derivatives
Intermediate Value Theorem 3.4 Graphs of Polynomial Functions
intersection 11.7 Probability
inverse cosine function 6.3 Inverse Trigonometric Functions
inverse of a radical function 3.8 Inverses and Radical Functions
inverse of a rational function 3.8 Inverses and Radical Functions
inverse sine function 6.3 Inverse Trigonometric Functions
inverse tangent function 6.3 Inverse Trigonometric Functions
inverse variation 3.9 Modeling Using Variation
inverse variations 3.9 Modeling Using Variation
inversely proportional 3.9 Modeling Using Variation
invertible functions 3.8 Inverses and Radical Functions
J
jump discontinuity 12.3 Continuity
L
least common denominator (LCD) 12.2 Finding Limits: Properties of Limits
least squares regression 2.4 Fitting Linear Models to Data
linear relationship 2.4 Fitting Linear Models to Data
linear speed 5.1 Angles
long division 3.5 Dividing Polynomials
lower limit of summation 11.4 Series and Their Notations
P
parallelograms 8.8 Vectors
partial fraction 9.4 Partial Fractions
partial fraction decomposition 9.4 Partial Fractions, 9.4 Partial Fractions
Pascal's Triangle 11.6 Binomial Theorem
perpendicular lines 2.2 Graphs of Linear Functions
point-slope form 2.1 Linear Functions
point-slope formula 10.2 The Hyperbola
polar form of a complex number 8.5 Polar Form of Complex Numbers
position vector 8.8 Vectors, 8.8 Vectors
positive angle 5.1 Angles, 5.1 Angles
probability 11.7 Probability
probability model 11.7 Probability
product of two matrices 9.5 Matrices and Matrix Operations
properties of determinants 9.8 Solving Systems with Cramer's Rule
R
radian measure 5.1 Angles, 5.1 Angles, 5.1 Angles
reciprocal function 3.7 Rational Functions
Restricting the domain 1.7 Inverse Functions
resultant 8.8 Vectors
S
sample space 11.7 Probability
SAS (side-angle-side) triangle 8.2 Non-right Triangles: Law of Cosines
secant line 12.4 Derivatives
sector of a circle 5.1 Angles
set-builder notation 1.2 Domain and Range
slope of the curve 12.4 Derivatives
slope of the tangent 12.4 Derivatives
slope-intercept form 2.1 Linear Functions
solving systems of linear equations 9.1 Systems of Linear Equations: Two Variables
SSS (side-side-side) triangle 8.2 Non-right Triangles: Law of Cosines
standard form of a quadratic function 3.2 Quadratic Functions
standard position 5.1 Angles, 5.1 Angles, 8.8 Vectors
stepwise function 12.3 Continuity
sum and difference formulas for cosine 7.2 Sum and Difference Identities
sum and difference formulas for sine 7.2 Sum and Difference Identities
sum and difference formulas for tangent 7.2 Sum and Difference Identities
summation notation 11.4 Series and Their Notations
system of three equations in three variables 9.8 Solving Systems with Cramer's Rule
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