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Precalculus

Index

PrecalculusIndex
  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 maximum 1.3 Rates of Change and Behavior of Graphs
absolute minimum 1.3 Rates of Change and Behavior of Graphs
absolute value 1.2 Domain and Range, 1.6 Absolute Value Functions
absolute value equation 1.6 Absolute Value Functions
absolute value functions 1.6 Absolute Value Functions, 1.6 Absolute Value Functions
absolute value inequality 1.6 Absolute Value Functions
addition method 9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables
Addition Principle 11.5 Counting Principles
adjacent side 5.4 Right Triangle Trigonometry
altitude 8.1 Non-right Triangles: Law of Sines
ambiguous case 8.1 Non-right Triangles: Law of Sines
amplitude 6.1 Graphs of the Sine and Cosine Functions, 7.6 Modeling with Trigonometric Functions, 7.6 Modeling with Trigonometric Functions
angle 5.1 Angles, 5.2 Unit Circle: Sine and Cosine Functions
angle of depression 5.4 Right Triangle Trigonometry
angle of elevation 5.4 Right Triangle Trigonometry, 8.1 Non-right Triangles: Law of Sines
angle of rotation 10.4 Rotation of Axes
angular speed 5.1 Angles
annual interest 11.4 Series and Their Notations
annual percentage rate (APR) 4.1 Exponential Functions
annuity 11.4 Series and Their Notations
apoapsis 10.5 Conic Sections in Polar Coordinates
arc 5.1 Angles
arc length 5.1 Angles, 5.1 Angles, 5.2 Unit Circle: Sine and Cosine Functions
arccosine 6.3 Inverse Trigonometric Functions
Archimedes’ spiral 8.4 Polar Coordinates: Graphs
arcsine 6.3 Inverse Trigonometric Functions
arctangent 6.3 Inverse Trigonometric Functions
area of a circle 3.3 Power Functions and Polynomial Functions
area of a sector 5.1 Angles, 5.1 Angles
argument 8.5 Polar Form of Complex Numbers
arithmetic sequence 11.2 Arithmetic Sequences, 11.2 Arithmetic Sequences, 11.2 Arithmetic Sequences, 11.2 Arithmetic Sequences, 11.4 Series and Their Notations
arithmetic series 11.4 Series and Their Notations
arrow notation 3.7 Rational Functions
asymptotes 10.2 The Hyperbola
augmented matrix 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.7 Solving Systems with Inverses
average rate of change 1.3 Rates of Change and Behavior of Graphs, 12.4 Derivatives
axes of symmetry 10.2 The Hyperbola
axis of symmetry 3.2 Quadratic Functions, 3.2 Quadratic Functions, 10.3 The Parabola, 10.3 The Parabola
B
binomial 3.5 Dividing Polynomials
binomial coefficient 11.6 Binomial Theorem
binomial expansion 11.6 Binomial Theorem, 11.6 Binomial Theorem
Binomial Theorem 11.6 Binomial Theorem
break-even point 9.1 Systems of Linear Equations: Two Variables
C
cardioid 8.4 Polar Coordinates: Graphs
carrying capacity 4.7 Exponential and Logarithmic Models
Cartesian equation 8.3 Polar Coordinates
Celsius 1.7 Inverse Functions
center of a hyperbola 10.2 The Hyperbola
center of an ellipse 10.1 The Ellipse
central rectangle 10.2 The Hyperbola
change-of-base formula 4.5 Logarithmic Properties, 4.5 Logarithmic Properties
circle 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
circular motion 6.1 Graphs of the Sine and Cosine Functions
circumference 5.1 Angles
co-vertex 10.1 The Ellipse
co-vertices 10.1 The Ellipse
coefficient 3.3 Power Functions and Polynomial Functions, 3.6 Zeros of Polynomial Functions
coefficient matrix 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
cofunction 7.2 Sum and Difference Identities
cofunction identities 5.4 Right Triangle Trigonometry, 7.2 Sum and Difference Identities
column 9.5 Matrices and Matrix Operations
column matrix 9.5 Matrices and Matrix Operations
combinations 11.5 Counting Principles, 11.6 Binomial Theorem
combining functions 1.4 Composition of Functions
common base 4.6 Exponential and Logarithmic Equations
common difference 11.2 Arithmetic Sequences, 11.4 Series and Their Notations
common logarithm 4.3 Logarithmic Functions
common ratio 11.3 Geometric Sequences, 11.4 Series and Their Notations
commutative 1.4 Composition of Functions
complement of an event 11.7 Probability
complex conjugate 3.1 Complex Numbers, 3.1 Complex Numbers
Complex Conjugate Theorem 3.6 Zeros of Polynomial Functions
complex number 3.1 Complex Numbers, 8.5 Polar Form of Complex Numbers
complex plane 3.1 Complex Numbers, 8.5 Polar Form of Complex Numbers
composite function 1.4 Composition of Functions
composition of functions 1.4 Composition of Functions
compound interest 4.1 Exponential Functions
compression 2.2 Graphs of Linear Functions, 4.2 Graphs of Exponential Functions, 4.4 Graphs of Logarithmic Functions
conic 10.1 The Ellipse, 10.2 The Hyperbola, 10.5 Conic Sections in Polar Coordinates
conic section 10.4 Rotation of Axes
conic sections 8.6 Parametric Equations
conjugate 12.2 Finding Limits: Properties of Limits
conjugate axis 10.2 The Hyperbola
consistent system 9.1 Systems of Linear Equations: Two Variables
constant of variation 3.9 Modeling Using Variation
constant rate of change 2.3 Modeling with Linear Functions
continuous 3.4 Graphs of Polynomial Functions
continuous function 3.3 Power Functions and Polynomial Functions, 12.3 Continuity
convex limaçons 8.4 Polar Coordinates: Graphs
coordinate plane 10.3 The Parabola
correlation coefficient 2.4 Fitting Linear Models to Data
cosecant 5.3 The Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
cosecant function 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions, 7.1 Solving Trigonometric Equations with Identities
cosine 7.4 Sum-to-Product and Product-to-Sum Formulas, 7.4 Sum-to-Product and Product-to-Sum Formulas
cosine function 5.2 Unit Circle: Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions
cost function 1.4 Composition of Functions, 9.1 Systems of Linear Equations: Two Variables
cotangent 5.3 The Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
cotangent function 6.2 Graphs of the Other Trigonometric Functions, 7.1 Solving Trigonometric Equations with Identities
coterminal angles 5.1 Angles, 5.1 Angles, 5.1 Angles
Cramer’s Rule 9.8 Solving Systems with Cramer's Rule, 9.8 Solving Systems with Cramer's Rule, 9.8 Solving Systems with Cramer's Rule, 9.8 Solving Systems with Cramer's Rule
cube root 3.3 Power Functions and Polynomial Functions
cubic functions 3.8 Inverses and Radical Functions
curvilinear path 8.6 Parametric Equations
D
damped harmonic motion 7.6 Modeling with Trigonometric Functions, 7.6 Modeling with Trigonometric Functions
De Moivre 8.5 Polar Form of Complex Numbers
De Moivre’s Theorem 8.5 Polar Form of Complex Numbers, 8.5 Polar Form of Complex Numbers
decompose a composite function 1.4 Composition of Functions
decomposition 9.4 Partial Fractions
decreasing function 1.3 Rates of Change and Behavior of Graphs, 2.1 Linear Functions
decreasing linear function 2.1 Linear Functions
degenerate conic sections 10.4 Rotation of Axes
degree 3.3 Power Functions and Polynomial Functions, 5.1 Angles
dependent system 9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables, 9.2 Systems of Linear Equations: Three Variables
dependent variable 1.1 Functions and Function Notation
derivative 12.4 Derivatives, 12.4 Derivatives, 12.4 Derivatives, 12.4 Derivatives, 12.4 Derivatives
Descartes 8.5 Polar Form of Complex Numbers
Descartes’ Rule of Signs 3.6 Zeros of Polynomial Functions
determinant 9.8 Solving Systems with Cramer's Rule, 9.8 Solving Systems with Cramer's Rule, 9.8 Solving Systems with Cramer's Rule
difference quotient 12.4 Derivatives
differentiable 12.4 Derivatives
dimpled limaçons 8.4 Polar Coordinates: Graphs
direct variation 3.9 Modeling Using Variation
directrix 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates
discontinuous 12.3 Continuity
discontinuous function 12.3 Continuity
displacement 5.1 Angles
distance formula 7.2 Sum and Difference Identities, 10.2 The Hyperbola, 10.3 The Parabola
diverges 11.4 Series and Their Notations
dividend 3.5 Dividing Polynomials
Division Algorithm 3.5 Dividing Polynomials, 3.6 Zeros of Polynomial Functions
divisor 3.5 Dividing Polynomials
domain 1.1 Functions and Function Notation, 1.1 Functions and Function Notation, 1.2 Domain and Range, 1.2 Domain and Range, 1.2 Domain and Range, 1.2 Domain and Range, 6.3 Inverse Trigonometric Functions, 6.3 Inverse Trigonometric Functions
domain and range 1.2 Domain and Range, 1.2 Domain and Range
domain of a composite function 1.4 Composition of Functions
dot product 8.8 Vectors
double-angle formulas 7.3 Double-Angle, Half-Angle, and Reduction Formulas, 7.3 Double-Angle, Half-Angle, and Reduction Formulas
doubling time 4.7 Exponential and Logarithmic Models
Dürer 8.4 Polar Coordinates: Graphs
E
eccentricity 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates
electrostatic force 1.3 Rates of Change and Behavior of Graphs
elimination 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
ellipse 8.7 Parametric Equations: Graphs, 8.7 Parametric Equations: Graphs, 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 10.1 The Ellipse, 10.1 The Ellipse, 10.1 The Ellipse, 10.1 The Ellipse, 10.1 The Ellipse, 10.3 The Parabola, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates
ellipsis 11.1 Sequences and Their Notations
end behavior 3.3 Power Functions and Polynomial Functions, 3.7 Rational Functions
endpoint 1.3 Rates of Change and Behavior of Graphs, 5.1 Angles
entry 9.5 Matrices and Matrix Operations
equation 1.1 Functions and Function Notation
Euler 8.5 Polar Form of Complex Numbers
even function 1.5 Transformation of Functions, 5.3 The Other Trigonometric Functions, 5.3 The Other Trigonometric Functions, 7.1 Solving Trigonometric Equations with Identities
even-odd identities 7.1 Solving Trigonometric Equations with Identities, 7.1 Solving Trigonometric Equations with Identities
event 11.7 Probability
experiment 11.7 Probability
explicit formula 11.1 Sequences and Their Notations, 11.1 Sequences and Their Notations, 11.1 Sequences and Their Notations, 11.2 Arithmetic Sequences, 11.3 Geometric Sequences
Exponential decay 4.1 Exponential Functions, 4.1 Exponential Functions, 4.2 Graphs of Exponential Functions, 4.7 Exponential and Logarithmic Models, 4.7 Exponential and Logarithmic Models, 4.7 Exponential and Logarithmic Models, 4.8 Fitting Exponential Models to Data
exponential equation 4.6 Exponential and Logarithmic Equations
exponential function 4.1 Exponential Functions
exponential growth 4.1 Exponential Functions, 4.1 Exponential Functions, 4.2 Graphs of Exponential Functions, 4.7 Exponential and Logarithmic Models, 4.7 Exponential and Logarithmic Models, 4.7 Exponential and Logarithmic Models
extraneous solution 4.6 Exponential and Logarithmic Equations
extrapolation 2.4 Fitting Linear Models to Data
F
Factor Theorem 3.6 Zeros of Polynomial Functions
factorial 11.1 Sequences and Their Notations
Fahrenheit 1.7 Inverse Functions
feasible region 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
finite arithmetic sequence 11.2 Arithmetic Sequences
finite sequence 11.1 Sequences and Their Notations
foci 10.1 The Ellipse, 10.1 The Ellipse, 10.1 The Ellipse, 10.2 The Hyperbola
focus 10.1 The Ellipse, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates
formula 1.1 Functions and Function Notation
function 1.1 Functions and Function Notation, 1.2 Domain and Range
function notation 1.1 Functions and Function Notation
Fundamental Counting Principle 11.5 Counting Principles
Fundamental Theorem of Algebra 3.6 Zeros of Polynomial Functions, 3.6 Zeros of Polynomial Functions
G
Gauss 8.5 Polar Form of Complex Numbers, 9.2 Systems of Linear Equations: Three Variables, 9.6 Solving Systems with Gaussian Elimination
Gaussian elimination 9.2 Systems of Linear Equations: Three Variables, 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination
general form 3.2 Quadratic Functions
general form of a quadratic function 3.2 Quadratic Functions
Generalized Pythagorean Theorem 8.2 Non-right Triangles: Law of Cosines
geometric sequence 11.3 Geometric Sequences, 11.4 Series and Their Notations
geometric series 11.4 Series and Their Notations
global maximum 3.4 Graphs of Polynomial Functions
global minimum 3.4 Graphs of Polynomial Functions
gravity 8.7 Parametric Equations: Graphs
H
half-angle formulas 7.3 Double-Angle, Half-Angle, and Reduction Formulas, 7.3 Double-Angle, Half-Angle, and Reduction Formulas
half-life 4.6 Exponential and Logarithmic Equations, 4.7 Exponential and Logarithmic Models
harmonic motion 7.6 Modeling with Trigonometric Functions
Heaviside method 9.4 Partial Fractions
Heron of Alexandria 8.2 Non-right Triangles: Law of Cosines
Heron’s formula 8.2 Non-right Triangles: Law of Cosines
horizontal asymptote 3.7 Rational Functions, 3.7 Rational Functions, 3.7 Rational Functions
horizontal compression 1.5 Transformation of Functions, 7.5 Solving Trigonometric Equations
horizontal line 2.2 Graphs of Linear Functions
horizontal line test 1.1 Functions and Function Notation
horizontal reflection 1.5 Transformation of Functions
horizontal shift 1.5 Transformation of Functions, 4.2 Graphs of Exponential Functions, 4.4 Graphs of Logarithmic Functions, 6.1 Graphs of the Sine and Cosine Functions
horizontal stretch 1.5 Transformation of Functions
hyperbola 10.2 The Hyperbola, 10.2 The Hyperbola, 10.2 The Hyperbola, 10.2 The Hyperbola, 10.2 The Hyperbola, 10.2 The Hyperbola, 10.2 The Hyperbola, 10.2 The Hyperbola, 10.3 The Parabola, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates
hypotenuse 5.4 Right Triangle Trigonometry
I
identities 5.2 Unit Circle: Sine and Cosine Functions, 5.3 The Other Trigonometric Functions
identity matrix 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
imaginary number 3.1 Complex Numbers
inconsistent system 9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables, 9.2 Systems of Linear Equations: Three Variables
increasing function 1.3 Rates of Change and Behavior of Graphs, 2.1 Linear Functions
increasing linear function 2.1 Linear Functions
independent system 9.1 Systems of Linear Equations: Two Variables
independent variable 1.1 Functions and Function Notation
index of summation 11.4 Series and Their Notations
inequality 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
infinite geometric sequence 11.4 Series and Their Notations
infinite sequence 11.1 Sequences and Their Notations
infinite series 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
input 1.1 Functions and Function Notation
instantaneous rate of change 12.4 Derivatives
instantaneous velocity 12.4 Derivatives
Intermediate Value Theorem 3.4 Graphs of Polynomial Functions
interpolation 2.4 Fitting Linear Models to Data
intersection 11.7 Probability
interval notation 1.2 Domain and Range, 1.3 Rates of Change and Behavior of Graphs
inverse cosine function 6.3 Inverse Trigonometric Functions
inverse function 1.7 Inverse Functions, 3.8 Inverses and Radical Functions, 3.8 Inverses and Radical Functions
inverse matrix 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
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 trigonometric functions 6.3 Inverse Trigonometric Functions, 6.3 Inverse Trigonometric Functions, 6.3 Inverse Trigonometric Functions, 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
invertible matrix 9.7 Solving Systems with Inverses, 9.8 Solving Systems with Cramer's Rule
J
joint variation 3.9 Modeling Using Variation
jump discontinuity 12.3 Continuity
K
Kronecker 8.5 Polar Form of Complex Numbers
L
latus rectum 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola
Law of Cosines 8.2 Non-right Triangles: Law of Cosines, 8.2 Non-right Triangles: Law of Cosines
Law of Sines 8.1 Non-right Triangles: Law of Sines, 8.2 Non-right Triangles: Law of Cosines
leading coefficient 3.3 Power Functions and Polynomial Functions
leading term 3.3 Power Functions and Polynomial Functions
least common denominator (LCD) 12.2 Finding Limits: Properties of Limits
least squares regression 2.4 Fitting Linear Models to Data
left-hand limit 12.1 Finding Limits: Numerical and Graphical Approaches, 12.3 Continuity
lemniscate 8.4 Polar Coordinates: Graphs
limit 12.1 Finding Limits: Numerical and Graphical Approaches, 12.1 Finding Limits: Numerical and Graphical Approaches, 12.1 Finding Limits: Numerical and Graphical Approaches, 12.2 Finding Limits: Properties of Limits, 12.2 Finding Limits: Properties of Limits, 12.2 Finding Limits: Properties of Limits, 12.2 Finding Limits: Properties of Limits, 12.2 Finding Limits: Properties of Limits, 12.2 Finding Limits: Properties of Limits
Linear Factorization Theorem 3.6 Zeros of Polynomial Functions, 3.6 Zeros of Polynomial Functions
linear function 2.1 Linear Functions, 2.3 Modeling with Linear Functions
linear growth 4.1 Exponential Functions
linear model 2.3 Modeling with Linear Functions, 2.4 Fitting Linear Models to Data
linear relationship 2.4 Fitting Linear Models to Data
linear speed 5.1 Angles
local extrema 1.3 Rates of Change and Behavior of Graphs
local maximum 1.3 Rates of Change and Behavior of Graphs, 3.4 Graphs of Polynomial Functions
local minimum 1.3 Rates of Change and Behavior of Graphs, 3.4 Graphs of Polynomial Functions
logarithm 4.3 Logarithmic Functions
logarithmic equation 4.6 Exponential and Logarithmic Equations
logarithmic model 4.8 Fitting Exponential Models to Data
logistic growth model 4.7 Exponential and Logarithmic Models
long division 3.5 Dividing Polynomials
lower limit of summation 11.4 Series and Their Notations
M
magnitude 1.2 Domain and Range, 1.5 Transformation of Functions, 8.5 Polar Form of Complex Numbers, 8.8 Vectors
main diagonal 9.6 Solving Systems with Gaussian Elimination
major and minor axes 10.1 The Ellipse
major axis 10.1 The Ellipse, 10.1 The Ellipse
marginal cost 12.4 Derivatives
matrix 9.5 Matrices and Matrix Operations, 9.5 Matrices and Matrix Operations, 9.6 Solving Systems with Gaussian Elimination
matrix multiplication 9.5 Matrices and Matrix Operations, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
matrix operations 9.5 Matrices and Matrix Operations
maximum value 3.2 Quadratic Functions
measure of an angle 5.1 Angles
midline 6.1 Graphs of the Sine and Cosine Functions, 7.6 Modeling with Trigonometric Functions
minimum value 3.2 Quadratic Functions
minor axis 10.1 The Ellipse
model breakdown 2.4 Fitting Linear Models to Data
modeling 2.3 Modeling with Linear Functions
modulus 1.2 Domain and Range, 8.5 Polar Form of Complex Numbers
Multiplication Principle 11.5 Counting Principles
multiplicative inverse 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
multiplicative inverse of a matrix 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
multiplicity 3.4 Graphs of Polynomial Functions, 3.4 Graphs of Polynomial Functions
mutually exclusive events 11.7 Probability
N
n factorial 11.1 Sequences and Their Notations
natural logarithm 4.3 Logarithmic Functions, 4.6 Exponential and Logarithmic Equations
natural numbers 1.1 Functions and Function Notation
negative angle 5.1 Angles, 5.1 Angles, 5.2 Unit Circle: Sine and Cosine Functions
Newton’s Law of Cooling 4.7 Exponential and Logarithmic Models
nominal rate 4.1 Exponential Functions
non-right triangles 8.1 Non-right Triangles: Law of Sines
nondegenerate conic sections 10.4 Rotation of Axes
nonlinear inequality 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
nth partial sum 11.4 Series and Their Notations
nth root of a complex number 8.5 Polar Form of Complex Numbers
nth term of the sequence 11.1 Sequences and Their Notations, 11.1 Sequences and Their Notations
O
oblique triangle 8.1 Non-right Triangles: Law of Sines
odd function 1.5 Transformation of Functions, 5.3 The Other Trigonometric Functions, 5.3 The Other Trigonometric Functions, 7.1 Solving Trigonometric Equations with Identities
one-loop limaçon 8.4 Polar Coordinates: Graphs
one-to-one 3.8 Inverses and Radical Functions, 4.2 Graphs of Exponential Functions, 4.3 Logarithmic Functions, 4.5 Logarithmic Properties, 4.5 Logarithmic Properties
one-to-one function 1.1 Functions and Function Notation, 1.7 Inverse Functions, 6.3 Inverse Trigonometric Functions
opposite side 5.4 Right Triangle Trigonometry
order of magnitude 4.7 Exponential and Logarithmic Models
ordered pair 1.1 Functions and Function Notation, 1.2 Domain and Range
ordered triple 9.2 Systems of Linear Equations: Three Variables
origin 1.6 Absolute Value Functions
outcomes 11.7 Probability
output 1.1 Functions and Function Notation
P
parabola 3.2 Quadratic Functions, 3.2 Quadratic Functions, 8.7 Parametric Equations: Graphs, 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates
parallel lines 2.2 Graphs of Linear Functions
parallelograms 8.8 Vectors
parameter 8.6 Parametric Equations
parametric equations 8.6 Parametric Equations, 8.7 Parametric Equations: Graphs, 8.7 Parametric Equations: Graphs
parametric form 8.7 Parametric Equations: Graphs
parent function 4.4 Graphs of Logarithmic Functions
partial fraction 9.4 Partial Fractions
partial fraction decomposition 9.4 Partial Fractions, 9.4 Partial Fractions
Pascal 8.4 Polar Coordinates: Graphs
Pascal's Triangle 11.6 Binomial Theorem
periapsis 10.5 Conic Sections in Polar Coordinates
period 5.3 The Other Trigonometric Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions, 7.5 Solving Trigonometric Equations, 7.6 Modeling with Trigonometric Functions
periodic function 5.3 The Other Trigonometric Functions, 6.1 Graphs of the Sine and Cosine Functions
periodic motion 7.6 Modeling with Trigonometric Functions, 7.6 Modeling with Trigonometric Functions
permutation 11.5 Counting Principles
perpendicular lines 2.2 Graphs of Linear Functions
pH 4.5 Logarithmic Properties
phase shift 6.1 Graphs of the Sine and Cosine Functions
piecewise function 1.2 Domain and Range, 12.3 Continuity, 12.3 Continuity, 12.3 Continuity
piecewise functions 11.1 Sequences and Their Notations
point-slope form 2.1 Linear Functions
point-slope formula 10.2 The Hyperbola
polar axis 8.3 Polar Coordinates
polar coordinates 8.3 Polar Coordinates, 8.3 Polar Coordinates, 8.3 Polar Coordinates, 8.4 Polar Coordinates: Graphs
polar equation 8.3 Polar Coordinates, 8.4 Polar Coordinates: Graphs, 8.4 Polar Coordinates: Graphs, 10.5 Conic Sections in Polar Coordinates
polar form 8.5 Polar Form of Complex Numbers
polar form of a complex number 8.5 Polar Form of Complex Numbers
polar form of a conic 10.5 Conic Sections in Polar Coordinates
polar grid 8.3 Polar Coordinates, 8.3 Polar Coordinates
pole 8.3 Polar Coordinates
polynomial 3.6 Zeros of Polynomial Functions, 12.3 Continuity
polynomial function 3.3 Power Functions and Polynomial Functions, 3.4 Graphs of Polynomial Functions, 3.4 Graphs of Polynomial Functions, 3.4 Graphs of Polynomial Functions
position vector 8.8 Vectors, 8.8 Vectors
positive angle 5.1 Angles, 5.1 Angles
power function 3.3 Power Functions and Polynomial Functions
power rule for logarithms 4.5 Logarithmic Properties, 4.5 Logarithmic Properties
probability 11.7 Probability
probability model 11.7 Probability
product of two matrices 9.5 Matrices and Matrix Operations
product rule for logarithms 4.5 Logarithmic Properties, 4.5 Logarithmic Properties
product-to-sum formulas 7.4 Sum-to-Product and Product-to-Sum Formulas, 7.4 Sum-to-Product and Product-to-Sum Formulas
profit function 9.1 Systems of Linear Equations: Two Variables
properties of determinants 9.8 Solving Systems with Cramer's Rule
properties of limits 12.2 Finding Limits: Properties of Limits
Proxima Centauri 4.7 Exponential and Logarithmic Models
Pythagoras 8.5 Polar Form of Complex Numbers
Pythagorean Identities 7.1 Solving Trigonometric Equations with Identities, 7.1 Solving Trigonometric Equations with Identities
Pythagorean Identity 5.2 Unit Circle: Sine and Cosine Functions, 5.2 Unit Circle: Sine and Cosine Functions, 5.3 The Other Trigonometric Functions, 7.2 Sum and Difference Identities
Pythagorean Theorem 7.3 Double-Angle, Half-Angle, and Reduction Formulas, 7.5 Solving Trigonometric Equations, 8.2 Non-right Triangles: Law of Cosines, 8.7 Parametric Equations: Graphs
Q
quadrantal angle 5.2 Unit Circle: Sine and Cosine Functions
quadratic 9.4 Partial Fractions, 9.4 Partial Fractions
quadratic equation 7.5 Solving Trigonometric Equations
quadratic formula 3.2 Quadratic Functions, 7.5 Solving Trigonometric Equations
quadratic function 3.2 Quadratic Functions, 3.2 Quadratic Functions
quotient 3.5 Dividing Polynomials
quotient identities 7.1 Solving Trigonometric Equations with Identities, 7.1 Solving Trigonometric Equations with Identities
quotient rule for logarithms 4.5 Logarithmic Properties
R
radian 5.1 Angles, 5.1 Angles, 5.1 Angles
radian measure 5.1 Angles, 5.1 Angles, 5.1 Angles
radical functions 3.8 Inverses and Radical Functions
radiocarbon dating 4.7 Exponential and Logarithmic Models
range 1.1 Functions and Function Notation, 6.3 Inverse Trigonometric Functions
rate of change 1.3 Rates of Change and Behavior of Graphs, 2.3 Modeling with Linear Functions
rational expression 9.4 Partial Fractions, 9.4 Partial Fractions, 9.4 Partial Fractions
rational function 3.7 Rational Functions, 3.7 Rational Functions, 3.7 Rational Functions, 12.2 Finding Limits: Properties of Limits
Rational Zero Theorem 3.6 Zeros of Polynomial Functions, 3.6 Zeros of Polynomial Functions
ray 5.1 Angles
reciprocal 1.7 Inverse Functions, 3.3 Power Functions and Polynomial Functions
reciprocal function 3.7 Rational Functions
reciprocal identities 7.1 Solving Trigonometric Equations with Identities, 7.1 Solving Trigonometric Equations with Identities
reciprocal identity 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
rectangular coordinates 8.3 Polar Coordinates, 8.3 Polar Coordinates, 8.3 Polar Coordinates
rectangular equation 8.3 Polar Coordinates, 8.6 Parametric Equations
rectangular form 8.5 Polar Form of Complex Numbers, 8.7 Parametric Equations: Graphs
recursive formula 11.1 Sequences and Their Notations, 11.2 Arithmetic Sequences, 11.2 Arithmetic Sequences, 11.3 Geometric Sequences
reduction formulas 7.3 Double-Angle, Half-Angle, and Reduction Formulas, 7.3 Double-Angle, Half-Angle, and Reduction Formulas
reference angle 5.1 Angles, 5.2 Unit Circle: Sine and Cosine Functions, 5.2 Unit Circle: Sine and Cosine Functions, 5.2 Unit Circle: Sine and Cosine Functions, 5.3 The Other Trigonometric Functions
reflection 4.2 Graphs of Exponential Functions, 4.4 Graphs of Logarithmic Functions
regression analysis 4.8 Fitting Exponential Models to Data, 4.8 Fitting Exponential Models to Data, 4.8 Fitting Exponential Models to Data
relation 1.1 Functions and Function Notation
remainder 3.5 Dividing Polynomials
Remainder Theorem 3.6 Zeros of Polynomial Functions
removable discontinuity 3.7 Rational Functions, 3.7 Rational Functions, 12.3 Continuity
Restricting the domain 1.7 Inverse Functions
resultant 8.8 Vectors
revenue function 9.1 Systems of Linear Equations: Two Variables
Richter Scale 4.3 Logarithmic Functions
right triangle 6.3 Inverse Trigonometric Functions
right triangles 5.4 Right Triangle Trigonometry
right-hand limit 12.1 Finding Limits: Numerical and Graphical Approaches, 12.3 Continuity
roots 3.2 Quadratic Functions
rose curve 8.4 Polar Coordinates: Graphs
row 9.5 Matrices and Matrix Operations
row matrix 9.5 Matrices and Matrix Operations
row operations 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
row-echelon form 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination
row-equivalent 9.6 Solving Systems with Gaussian Elimination
S
sample space 11.7 Probability
SAS (side-angle-side) triangle 8.2 Non-right Triangles: Law of Cosines
scalar 8.8 Vectors, 9.5 Matrices and Matrix Operations
scalar multiple 8.8 Vectors, 9.5 Matrices and Matrix Operations
Scalar multiplication 8.8 Vectors, 9.5 Matrices and Matrix Operations
scatter plot 2.4 Fitting Linear Models to Data
secant 5.3 The Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
secant function 6.2 Graphs of the Other Trigonometric Functions
secant line 12.4 Derivatives
sector of a circle 5.1 Angles
sequence 11.1 Sequences and Their Notations, 11.1 Sequences and Their Notations, 11.2 Arithmetic Sequences, 12.1 Finding Limits: Numerical and Graphical Approaches
series 11.4 Series and Their Notations
set-builder notation 1.2 Domain and Range
sigma 11.4 Series and Their Notations
simple harmonic motion 7.6 Modeling with Trigonometric Functions, 7.6 Modeling with Trigonometric Functions
sine 7.1 Solving Trigonometric Equations with Identities, 7.4 Sum-to-Product and Product-to-Sum Formulas, 7.4 Sum-to-Product and Product-to-Sum Formulas
sine function 5.2 Unit Circle: Sine and Cosine Functions, 5.3 The Other Trigonometric Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions, 6.1 Graphs of the Sine and Cosine Functions
sinusoidal function 6.1 Graphs of the Sine and Cosine Functions, 7.6 Modeling with Trigonometric Functions
slope 2.1 Linear Functions, 2.1 Linear Functions
slope of the curve 12.4 Derivatives
slope of the tangent 12.4 Derivatives
slope-intercept form 2.1 Linear Functions
smooth curve 3.3 Power Functions and Polynomial Functions
solution set 9.2 Systems of Linear Equations: Three Variables
solving systems of linear equations 9.1 Systems of Linear Equations: Two Variables
special angles 5.2 Unit Circle: Sine and Cosine Functions, 5.4 Right Triangle Trigonometry, 7.2 Sum and Difference Identities
square matrix 9.5 Matrices and Matrix Operations, 9.8 Solving Systems with Cramer's Rule
SSA (side-side-angle) 8.1 Non-right Triangles: Law of Sines
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
stretch 4.2 Graphs of Exponential Functions
stretching/compressing factor 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
substitution method 9.1 Systems of Linear Equations: Two Variables
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
sum-to-product formulas 7.4 Sum-to-Product and Product-to-Sum Formulas, 7.4 Sum-to-Product and Product-to-Sum Formulas
summation notation 11.4 Series and Their Notations
surface area 3.8 Inverses and Radical Functions
symmetry test 8.4 Polar Coordinates: Graphs
synthetic division 3.5 Dividing Polynomials, 3.6 Zeros of Polynomial Functions
system of equations 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.7 Solving Systems with Inverses
system of linear equations 2.3 Modeling with Linear Functions, 9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables
system of nonlinear equations 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of nonlinear inequalities 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of three equations in three variables 9.8 Solving Systems with Cramer's Rule
T
tangent 5.3 The Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
tangent function 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions, 7.1 Solving Trigonometric Equations with Identities
tangent line 12.4 Derivatives
term 11.1 Sequences and Their Notations, 11.2 Arithmetic Sequences
term of a polynomial function 3.3 Power Functions and Polynomial Functions
terminal point 8.8 Vectors, 8.8 Vectors
terminal side 5.1 Angles
transformation 1.5 Transformation of Functions
transformations 2.2 Graphs of Linear Functions
translation 10.1 The Ellipse
transverse axis 10.2 The Hyperbola
trigonometric equations 8.6 Parametric Equations
trigonometric functions 5.4 Right Triangle Trigonometry
trigonometric identities 8.2 Non-right Triangles: Law of Cosines
turning point 3.3 Power Functions and Polynomial Functions, 3.4 Graphs of Polynomial Functions
two-sided limit 12.1 Finding Limits: Numerical and Graphical Approaches, 12.4 Derivatives
U
union of two events 11.7 Probability
unit circle 5.1 Angles, 5.2 Unit Circle: Sine and Cosine Functions, 5.2 Unit Circle: Sine and Cosine Functions, 5.2 Unit Circle: Sine and Cosine Functions, 5.2 Unit Circle: Sine and Cosine Functions, 5.3 The Other Trigonometric Functions, 5.4 Right Triangle Trigonometry, 7.5 Solving Trigonometric Equations
unit vector 8.8 Vectors
upper limit of summation 11.4 Series and Their Notations
upper triangular form 9.2 Systems of Linear Equations: Three Variables
V
varies directly 3.9 Modeling Using Variation
varies inversely 3.9 Modeling Using Variation
vector 8.8 Vectors
vector addition 8.8 Vectors
velocity 12.4 Derivatives, 12.4 Derivatives
vertex 3.2 Quadratic Functions, 5.1 Angles, 10.1 The Ellipse, 10.1 The Ellipse, 10.3 The Parabola, 10.3 The Parabola
vertex form of a quadratic function 3.2 Quadratic Functions
vertical asymptote 3.7 Rational Functions, 3.7 Rational Functions, 3.7 Rational Functions, 6.3 Inverse Trigonometric Functions
vertical compression 1.5 Transformation of Functions
vertical line 2.2 Graphs of Linear Functions
vertical line test 1.1 Functions and Function Notation
vertical reflection 1.5 Transformation of Functions
vertical shift 1.5 Transformation of Functions, 2.2 Graphs of Linear Functions, 4.2 Graphs of Exponential Functions, 4.4 Graphs of Logarithmic Functions, 4.7 Exponential and Logarithmic Models, 6.1 Graphs of the Sine and Cosine Functions
vertical stretch 1.5 Transformation of Functions, 2.2 Graphs of Linear Functions, 4.4 Graphs of Logarithmic Functions
vertical tangent 12.4 Derivatives
vertices 10.1 The Ellipse, 10.1 The Ellipse
volume of a sphere 3.3 Power Functions and Polynomial Functions
X
x-intercept 2.2 Graphs of Linear Functions
Y
y-intercept 2.1 Linear Functions, 2.2 Graphs of Linear Functions
Z
zeros 3.2 Quadratic Functions, 3.4 Graphs of Polynomial Functions, 3.4 Graphs of Polynomial Functions, 3.6 Zeros of Polynomial Functions, 8.4 Polar Coordinates: Graphs
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