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  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 Equations
    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
absolute value equation1.6 Absolute Value Functions
absolute value inequality1.6 Absolute Value Functions
Addition Principle11.5 Counting Principles
angle of rotation10.4 Rotation of Axes
angular speed5.1 Angles
annual percentage rate (APR)4.1 Exponential Functions
Archimedes’ spiral8.4 Polar Coordinates: Graphs
area of a sector5.1 Angles, 5.1 Angles
axes of symmetry10.2 The Hyperbola
C
Cartesian equation8.3 Polar Coordinates
center of a hyperbola10.2 The Hyperbola
center of an ellipse10.1 The Ellipse
central rectangle10.2 The Hyperbola
circumference5.1 Angles
co-vertices10.1 The Ellipse
combining functions1.4 Composition of Functions
complement of an event 11.7 Probability
Complex Conjugate Theorem3.6 Zeros of Polynomial Functions
composition of functions1.4 Composition of Functions
compound interest4.1 Exponential Functions
conjugate axis10.2 The Hyperbola
constant of variation3.9 Modeling Using Variation
constant rate of change2.3 Modeling with Linear Functions
coordinate plane10.3 The Parabola
correlation coefficient2.4 Fitting Linear Models to Data
coterminal angles5.1 Angles, 5.1 Angles, 5.1 Angles
curvilinear path8.6 Parametric Equations
D
decompose a composite function1.4 Composition of Functions
decreasing linear function2.1 Linear Functions
degenerate conic sections10.4 Rotation of Axes
Descartes’ Rule of Signs3.6 Zeros of Polynomial Functions
difference quotient12.4 Derivatives
differentiable12.4 Derivatives
discontinuous12.3 Continuity
discontinuous function12.3 Continuity
displacement5.1 Angles
domain of a composite function1.4 Composition of Functions
dot product8.8 Vectors
E
exponential function4.1 Exponential Functions
I
imaginary number3.1 Complex Numbers
increasing linear function2.1 Linear Functions
infinite geometric sequence11.4 Series and Their Notations
initial point8.8 Vectors, 8.8 Vectors
initial side5.1 Angles
inner-loop limaçons8.4 Polar Coordinates: Graphs
instantaneous rate of change12.4 Derivatives
instantaneous velocity12.4 Derivatives
Intermediate Value Theorem3.4 Graphs of Polynomial Functions
intersection11.7 Probability
inverse of a radical function3.8 Inverses and Radical Functions
inverse of a rational function3.8 Inverses and Radical Functions
inverse tangent function6.3 Inverse Trigonometric Functions
inversely proportional3.9 Modeling Using Variation
J
jump discontinuity12.3 Continuity
L
least common denominator (LCD)12.2 Finding Limits: Properties of Limits
least squares regression2.4 Fitting Linear Models to Data
linear speed5.1 Angles
lower limit of summation11.4 Series and Their Notations
P
parallelograms8.8 Vectors
partial fraction9.4 Partial Fractions
partial fraction decomposition9.4 Partial Fractions, 9.4 Partial Fractions
Pascal's Triangle11.6 Binomial Theorem
point-slope form2.1 Linear Functions
point-slope formula10.2 The Hyperbola
polar form of a complex number8.5 Polar Form of Complex Numbers
position vector8.8 Vectors, 8.8 Vectors
positive angle5.1 Angles, 5.1 Angles
probability11.7 Probability
probability model11.7 Probability
product of two matrices9.5 Matrices and Matrix Operations
properties of determinants9.8 Solving Systems with Cramer's Rule
R
reciprocal function3.7 Rational Functions
Restricting the domain1.7 Inverse Functions
resultant8.8 Vectors
S
sample space11.7 Probability
SAS (side-angle-side) triangle8.2 Non-right Triangles: Law of Cosines
secant line12.4 Derivatives
sector of a circle5.1 Angles
set-builder notation1.2 Domain and Range
slope of the curve12.4 Derivatives
slope of the tangent12.4 Derivatives
slope-intercept form2.1 Linear Functions
solving systems of linear equations9.1 Systems of Linear Equations: Two Variables
SSS (side-side-side) triangle8.2 Non-right Triangles: Law of Cosines
standard form of a quadratic function3.2 Quadratic Functions
standard position5.1 Angles, 5.1 Angles, 8.8 Vectors
stepwise function12.3 Continuity
sum and difference formulas for cosine7.2 Sum and Difference Identities
sum and difference formulas for sine7.2 Sum and Difference Identities
sum and difference formulas for tangent7.2 Sum and Difference Identities
system of three equations in three variables9.8 Solving Systems with Cramer's Rule
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