Skip to ContentGo to accessibility page
OpenStax Logo
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 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
AAS (angle-angle-side)8.1 Non-right Triangles: Law of Sines
absolute maximum1.3 Rates of Change and Behavior of Graphs
absolute minimum1.3 Rates of Change and Behavior of Graphs
absolute value1.2 Domain and Range, 1.6 Absolute Value Functions
absolute value equation1.6 Absolute Value Functions
absolute value functions1.6 Absolute Value Functions, 1.6 Absolute Value Functions
absolute value inequality1.6 Absolute Value Functions
addition method9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables
Addition Principle11.5 Counting Principles
adjacent side5.4 Right Triangle Trigonometry
altitude8.1 Non-right Triangles: Law of Sines
ambiguous case8.1 Non-right Triangles: Law of Sines
amplitude6.1 Graphs of the Sine and Cosine Functions, 7.6 Modeling with Trigonometric Equations, 7.6 Modeling with Trigonometric Equations
angle5.1 Angles, 5.2 Unit Circle: Sine and Cosine Functions
angle of depression5.4 Right Triangle Trigonometry
angle of elevation5.4 Right Triangle Trigonometry, 8.1 Non-right Triangles: Law of Sines
angle of rotation10.4 Rotation of Axes
angular speed5.1 Angles
annual interest11.4 Series and Their Notations
annual percentage rate (APR)4.1 Exponential Functions
annuity11.4 Series and Their Notations
apoapsis10.5 Conic Sections in Polar Coordinates
arc5.1 Angles
arc length5.1 Angles, 5.1 Angles
arc length 5.2 Unit Circle: Sine and Cosine Functions
arccosine6.3 Inverse Trigonometric Functions
Archimedes’ spiral8.4 Polar Coordinates: Graphs
arcsine6.3 Inverse Trigonometric Functions
arctangent6.3 Inverse Trigonometric Functions
area of a circle3.3 Power Functions and Polynomial Functions
area of a sector5.1 Angles, 5.1 Angles
argument8.5 Polar Form of Complex Numbers
arithmetic sequence11.2 Arithmetic Sequences, 11.2 Arithmetic Sequences, 11.2 Arithmetic Sequences, 11.2 Arithmetic Sequences, 11.4 Series and Their Notations
arithmetic series11.4 Series and Their Notations
arrow notation3.7 Rational Functions
asymptotes10.2 The Hyperbola
augmented matrix9.6 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 change1.3 Rates of Change and Behavior of Graphs, 12.4 Derivatives
axes of symmetry10.2 The Hyperbola
axis of symmetry3.2 Quadratic Functions, 3.2 Quadratic Functions, 10.3 The Parabola, 10.3 The Parabola
B
binomial3.5 Dividing Polynomials
binomial coefficient 11.6 Binomial Theorem
binomial expansion11.6 Binomial Theorem, 11.6 Binomial Theorem
Binomial Theorem11.6 Binomial Theorem
break-even point9.1 Systems of Linear Equations: Two Variables
C
cardioid8.4 Polar Coordinates: Graphs
carrying capacity4.7 Exponential and Logarithmic Models
Cartesian equation8.3 Polar Coordinates
Celsius1.7 Inverse Functions
center of a hyperbola10.2 The Hyperbola
center of an ellipse10.1 The Ellipse
central rectangle10.2 The Hyperbola
change-of-base formula4.5 Logarithmic Properties, 4.5 Logarithmic Properties
circle9.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
circular motion6.1 Graphs of the Sine and Cosine Functions
circumference5.1 Angles
co-vertex10.1 The Ellipse
co-vertices10.1 The Ellipse
coefficient3.3 Power Functions and Polynomial Functions, 3.6 Zeros of Polynomial Functions
coefficient matrix9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
cofunction7.2 Sum and Difference Identities
cofunction identities5.4 Right Triangle Trigonometry, 7.2 Sum and Difference Identities
column9.5 Matrices and Matrix Operations
column matrix9.5 Matrices and Matrix Operations
combinations11.5 Counting Principles, 11.6 Binomial Theorem
combining functions1.4 Composition of Functions
common base4.6 Exponential and Logarithmic Equations
common difference11.2 Arithmetic Sequences, 11.4 Series and Their Notations
common logarithm4.3 Logarithmic Functions
common ratio11.3 Geometric Sequences, 11.4 Series and Their Notations
commutative1.4 Composition of Functions
complement of an event 11.7 Probability
complex conjugate3.1 Complex Numbers, 3.1 Complex Numbers
Complex Conjugate Theorem3.6 Zeros of Polynomial Functions
complex number3.1 Complex Numbers, 8.5 Polar Form of Complex Numbers
complex plane3.1 Complex Numbers, 8.5 Polar Form of Complex Numbers
composite function1.4 Composition of Functions
composition of functions1.4 Composition of Functions
compound interest4.1 Exponential Functions
compression2.2 Graphs of Linear Functions, 4.2 Graphs of Exponential Functions, 4.4 Graphs of Logarithmic Functions
conic10.1 The Ellipse, 10.2 The Hyperbola, 10.5 Conic Sections in Polar Coordinates
conic section10.4 Rotation of Axes
conic sections8.6 Parametric Equations
conjugate12.2 Finding Limits: Properties of Limits
conjugate axis10.2 The Hyperbola
consistent system9.1 Systems of Linear Equations: Two Variables
constant of variation3.9 Modeling Using Variation
constant rate of change2.3 Modeling with Linear Functions
continuous3.4 Graphs of Polynomial Functions
continuous function3.3 Power Functions and Polynomial Functions, 12.3 Continuity
convex limaçons8.4 Polar Coordinates: Graphs
coordinate plane10.3 The Parabola
correlation coefficient2.4 Fitting Linear Models to Data
cosecant5.3 The Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
cosecant function6.2 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
cosine7.4 Sum-to-Product and Product-to-Sum Formulas, 7.4 Sum-to-Product and Product-to-Sum Formulas
cosine function5.2 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 function1.4 Composition of Functions, 9.1 Systems of Linear Equations: Two Variables
cotangent5.3 The Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
cotangent function6.2 Graphs of the Other Trigonometric Functions, 7.1 Solving Trigonometric Equations with Identities
coterminal angles5.1 Angles, 5.1 Angles, 5.1 Angles
Cramer’s Rule9.8 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 root3.3 Power Functions and Polynomial Functions
cubic functions3.8 Inverses and Radical Functions
curvilinear path8.6 Parametric Equations
D
damped harmonic motion7.6 Modeling with Trigonometric Equations, 7.6 Modeling with Trigonometric Equations
De Moivre8.5 Polar Form of Complex Numbers
De Moivre’s Theorem8.5 Polar Form of Complex Numbers, 8.5 Polar Form of Complex Numbers
decompose a composite function1.4 Composition of Functions
decomposition9.4 Partial Fractions
decreasing function1.3 Rates of Change and Behavior of Graphs, 2.1 Linear Functions
decreasing linear function2.1 Linear Functions
degenerate conic sections10.4 Rotation of Axes
degree3.3 Power Functions and Polynomial Functions, 5.1 Angles
dependent system9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables, 9.2 Systems of Linear Equations: Three Variables
dependent variable1.1 Functions and Function Notation
derivative12.4 Derivatives, 12.4 Derivatives, 12.4 Derivatives, 12.4 Derivatives, 12.4 Derivatives
Descartes8.5 Polar Form of Complex Numbers
Descartes’ Rule of Signs3.6 Zeros of Polynomial Functions
determinant9.8 Solving Systems with Cramer's Rule, 9.8 Solving Systems with Cramer's Rule, 9.8 Solving Systems with Cramer's Rule
difference quotient12.4 Derivatives
differentiable12.4 Derivatives
dimpled limaçons8.4 Polar Coordinates: Graphs
direct variation3.9 Modeling Using Variation
directrix10.3 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
discontinuous12.3 Continuity
discontinuous function12.3 Continuity
displacement5.1 Angles
distance formula7.2 Sum and Difference Identities, 10.2 The Hyperbola, 10.3 The Parabola
diverges11.4 Series and Their Notations
dividend3.5 Dividing Polynomials
Division Algorithm3.5 Dividing Polynomials, 3.6 Zeros of Polynomial Functions
divisor3.5 Dividing Polynomials
domain1.1 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 range1.2 Domain and Range, 1.2 Domain and Range
domain of a composite function1.4 Composition of Functions
dot product8.8 Vectors
double-angle formulas7.3 Double-Angle, Half-Angle, and Reduction Formulas, 7.3 Double-Angle, Half-Angle, and Reduction Formulas
doubling time4.7 Exponential and Logarithmic Models
Dürer8.4 Polar Coordinates: Graphs
E
eccentricity10.5 Conic Sections in Polar Coordinates, 10.5 Conic Sections in Polar Coordinates
electrostatic force1.3 Rates of Change and Behavior of Graphs
elimination9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
ellipse8.7 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
ellipsis11.1 Sequences and Their Notations
end behavior3.3 Power Functions and Polynomial Functions, 3.7 Rational Functions
endpoint1.3 Rates of Change and Behavior of Graphs, 5.1 Angles
entry9.5 Matrices and Matrix Operations
equation1.1 Functions and Function Notation
Euler8.5 Polar Form of Complex Numbers
even function1.5 Transformation of Functions, 5.3 The Other Trigonometric Functions, 5.3 The Other Trigonometric Functions, 7.1 Solving Trigonometric Equations with Identities
even-odd identities7.1 Solving Trigonometric Equations with Identities, 7.1 Solving Trigonometric Equations with Identities
event11.7 Probability
experiment11.7 Probability
explicit formula11.1 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 decay4.1 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 equation4.6 Exponential and Logarithmic Equations
exponential function4.1 Exponential Functions
exponential growth4.1 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 solution4.6 Exponential and Logarithmic Equations
extrapolation2.4 Fitting Linear Models to Data
F
Factor Theorem3.6 Zeros of Polynomial Functions
factorial11.1 Sequences and Their Notations
Fahrenheit1.7 Inverse Functions
feasible region9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
finite arithmetic sequence11.2 Arithmetic Sequences
finite sequence11.1 Sequences and Their Notations
foci10.1 The Ellipse, 10.1 The Ellipse, 10.1 The Ellipse, 10.2 The Hyperbola
focus10.1 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
formula1.1 Functions and Function Notation
function1.1 Functions and Function Notation, 1.2 Domain and Range
function notation1.1 Functions and Function Notation
Fundamental Counting Principle11.5 Counting Principles
Fundamental Theorem of Algebra3.6 Zeros of Polynomial Functions, 3.6 Zeros of Polynomial Functions
G
Gauss8.5 Polar Form of Complex Numbers, 9.2 Systems of Linear Equations: Three Variables, 9.6 Solving Systems with Gaussian Elimination
Gaussian elimination9.2 Systems of Linear Equations: Three Variables, 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination
general form3.2 Quadratic Functions
general form of a quadratic function3.2 Quadratic Functions
Generalized Pythagorean Theorem8.2 Non-right Triangles: Law of Cosines
geometric sequence11.3 Geometric Sequences, 11.4 Series and Their Notations
geometric series11.4 Series and Their Notations
global maximum3.4 Graphs of Polynomial Functions
global minimum3.4 Graphs of Polynomial Functions
gravity8.7 Parametric Equations: Graphs
H
half-angle formulas7.3 Double-Angle, Half-Angle, and Reduction Formulas, 7.3 Double-Angle, Half-Angle, and Reduction Formulas
half-life4.6 Exponential and Logarithmic Equations, 4.7 Exponential and Logarithmic Models
harmonic motion7.6 Modeling with Trigonometric Equations
Heaviside method9.4 Partial Fractions
Heron of Alexandria8.2 Non-right Triangles: Law of Cosines
Heron’s formula8.2 Non-right Triangles: Law of Cosines
horizontal asymptote3.7 Rational Functions, 3.7 Rational Functions, 3.7 Rational Functions
horizontal compression1.5 Transformation of Functions, 7.5 Solving Trigonometric Equations
horizontal line2.2 Graphs of Linear Functions
horizontal line test1.1 Functions and Function Notation
horizontal reflection1.5 Transformation of Functions
horizontal shift1.5 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 stretch1.5 Transformation of Functions
hyperbola10.2 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
hypotenuse5.4 Right Triangle Trigonometry
I
identities5.2 Unit Circle: Sine and Cosine Functions, 5.3 The Other Trigonometric Functions
identity matrix9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
imaginary number3.1 Complex Numbers
inconsistent system9.1 Systems of Linear Equations: Two Variables, 9.1 Systems of Linear Equations: Two Variables, 9.2 Systems of Linear Equations: Three Variables
increasing function1.3 Rates of Change and Behavior of Graphs, 2.1 Linear Functions
increasing linear function2.1 Linear Functions
independent system9.1 Systems of Linear Equations: Two Variables
independent variable1.1 Functions and Function Notation
index of summation11.4 Series and Their Notations
inequality9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
infinite geometric sequence11.4 Series and Their Notations
infinite sequence11.1 Sequences and Their Notations
infinite series11.4 Series and Their Notations
initial point8.8 Vectors, 8.8 Vectors
initial side5.1 Angles
inner-loop limaçons8.4 Polar Coordinates: Graphs
input1.1 Functions and Function Notation
instantaneous rate of change12.4 Derivatives
instantaneous velocity12.4 Derivatives
Intermediate Value Theorem3.4 Graphs of Polynomial Functions
interpolation2.4 Fitting Linear Models to Data
intersection11.7 Probability
interval notation1.2 Domain and Range, 1.3 Rates of Change and Behavior of Graphs
inverse cosine function6.3 Inverse Trigonometric Functions
inverse function1.7 Inverse Functions, 3.8 Inverses and Radical Functions, 3.8 Inverses and Radical Functions
inverse matrix9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
inverse of a radical function3.8 Inverses and Radical Functions
inverse of a rational function3.8 Inverses and Radical Functions
inverse sine function6.3 Inverse Trigonometric Functions
inverse tangent function6.3 Inverse Trigonometric Functions
inverse trigonometric functions6.3 Inverse Trigonometric Functions, 6.3 Inverse Trigonometric Functions, 6.3 Inverse Trigonometric Functions, 6.3 Inverse Trigonometric Functions
inverse variation3.9 Modeling Using Variation
inverse variations3.9 Modeling Using Variation
inversely proportional3.9 Modeling Using Variation
invertible functions3.8 Inverses and Radical Functions
invertible matrix9.7 Solving Systems with Inverses, 9.8 Solving Systems with Cramer's Rule
J
joint variation3.9 Modeling Using Variation
jump discontinuity12.3 Continuity
K
Kronecker8.5 Polar Form of Complex Numbers
L
latus rectum10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola, 10.3 The Parabola
Law of Cosines8.2 Non-right Triangles: Law of Cosines, 8.2 Non-right Triangles: Law of Cosines
Law of Sines8.1 Non-right Triangles: Law of Sines, 8.2 Non-right Triangles: Law of Cosines
leading coefficient3.3 Power Functions and Polynomial Functions
leading term3.3 Power Functions and Polynomial Functions
least common denominator (LCD)12.2 Finding Limits: Properties of Limits
least squares regression2.4 Fitting Linear Models to Data
left-hand limit12.1 Finding Limits: Numerical and Graphical Approaches, 12.3 Continuity
lemniscate8.4 Polar Coordinates: Graphs
limit12.1 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 Theorem3.6 Zeros of Polynomial Functions, 3.6 Zeros of Polynomial Functions
linear function2.1 Linear Functions, 2.3 Modeling with Linear Functions
linear growth4.1 Exponential Functions
linear model2.3 Modeling with Linear Functions, 2.4 Fitting Linear Models to Data
linear relationship2.4 Fitting Linear Models to Data
linear speed5.1 Angles
local extrema1.3 Rates of Change and Behavior of Graphs
local maximum1.3 Rates of Change and Behavior of Graphs, 3.4 Graphs of Polynomial Functions
local minimum1.3 Rates of Change and Behavior of Graphs, 3.4 Graphs of Polynomial Functions
logarithm4.3 Logarithmic Functions
logarithmic equation4.6 Exponential and Logarithmic Equations
logarithmic model4.8 Fitting Exponential Models to Data
logistic growth model4.7 Exponential and Logarithmic Models
long division3.5 Dividing Polynomials
lower limit of summation11.4 Series and Their Notations
M
magnitude1.2 Domain and Range, 1.5 Transformation of Functions, 8.5 Polar Form of Complex Numbers, 8.8 Vectors
main diagonal9.6 Solving Systems with Gaussian Elimination
major and minor axes10.1 The Ellipse
major axis10.1 The Ellipse, 10.1 The Ellipse
marginal cost12.4 Derivatives
matrix9.5 Matrices and Matrix Operations, 9.5 Matrices and Matrix Operations, 9.6 Solving Systems with Gaussian Elimination
matrix multiplication9.5 Matrices and Matrix Operations, 9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
matrix operations9.5 Matrices and Matrix Operations
maximum value3.2 Quadratic Functions
measure of an angle5.1 Angles
midline6.1 Graphs of the Sine and Cosine Functions, 7.6 Modeling with Trigonometric Equations
minimum value3.2 Quadratic Functions
minor axis10.1 The Ellipse
model breakdown2.4 Fitting Linear Models to Data
modeling2.3 Modeling with Linear Functions
modulus1.2 Domain and Range, 8.5 Polar Form of Complex Numbers
Multiplication Principle11.5 Counting Principles
multiplicative inverse9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
multiplicative inverse of a matrix9.7 Solving Systems with Inverses, 9.7 Solving Systems with Inverses
multiplicity3.4 Graphs of Polynomial Functions, 3.4 Graphs of Polynomial Functions
mutually exclusive events11.7 Probability
N
n factorial11.1 Sequences and Their Notations
natural logarithm4.3 Logarithmic Functions, 4.6 Exponential and Logarithmic Equations
natural numbers1.1 Functions and Function Notation
negative angle5.1 Angles, 5.1 Angles, 5.2 Unit Circle: Sine and Cosine Functions
Newton’s Law of Cooling4.7 Exponential and Logarithmic Models
nominal rate4.1 Exponential Functions
non-right triangles8.1 Non-right Triangles: Law of Sines
nondegenerate conic sections10.4 Rotation of Axes
nonlinear inequality9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
nth partial sum11.4 Series and Their Notations
nth root of a complex number8.5 Polar Form of Complex Numbers
nth term of the sequence11.1 Sequences and Their Notations, 11.1 Sequences and Their Notations
O
oblique triangle8.1 Non-right Triangles: Law of Sines
odd function1.5 Transformation of Functions, 5.3 The Other Trigonometric Functions, 5.3 The Other Trigonometric Functions, 7.1 Solving Trigonometric Equations with Identities
one-loop limaçon8.4 Polar Coordinates: Graphs
one-to-one3.8 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 function1.1 Functions and Function Notation, 1.7 Inverse Functions, 6.3 Inverse Trigonometric Functions
opposite side5.4 Right Triangle Trigonometry
order of magnitude4.7 Exponential and Logarithmic Models
ordered pair1.1 Functions and Function Notation, 1.2 Domain and Range
ordered triple9.2 Systems of Linear Equations: Three Variables
origin1.6 Absolute Value Functions
outcomes11.7 Probability
output1.1 Functions and Function Notation
P
parabola3.2 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 lines2.2 Graphs of Linear Functions
parallelograms8.8 Vectors
parameter8.6 Parametric Equations
parametric equations8.6 Parametric Equations, 8.7 Parametric Equations: Graphs, 8.7 Parametric Equations: Graphs
parametric form8.7 Parametric Equations: Graphs
parent function4.4 Graphs of Logarithmic Functions
partial fraction9.4 Partial Fractions
partial fraction decomposition9.4 Partial Fractions, 9.4 Partial Fractions
Pascal8.4 Polar Coordinates: Graphs
Pascal's Triangle11.6 Binomial Theorem
periapsis10.5 Conic Sections in Polar Coordinates
period5.3 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 Equations
periodic function5.3 The Other Trigonometric Functions, 6.1 Graphs of the Sine and Cosine Functions
periodic motion7.6 Modeling with Trigonometric Equations, 7.6 Modeling with Trigonometric Equations
permutation11.5 Counting Principles
perpendicular lines2.2 Graphs of Linear Functions
pH4.5 Logarithmic Properties
phase shift6.1 Graphs of the Sine and Cosine Functions
piecewise function1.2 Domain and Range, 12.3 Continuity, 12.3 Continuity, 12.3 Continuity
piecewise functions11.1 Sequences and Their Notations
point-slope form2.1 Linear Functions
point-slope formula10.2 The Hyperbola
polar axis8.3 Polar Coordinates
polar coordinates8.3 Polar Coordinates, 8.3 Polar Coordinates, 8.3 Polar Coordinates, 8.4 Polar Coordinates: Graphs
polar equation8.3 Polar Coordinates, 8.4 Polar Coordinates: Graphs, 8.4 Polar Coordinates: Graphs, 10.5 Conic Sections in Polar Coordinates
polar form8.5 Polar Form of Complex Numbers
polar form of a complex number8.5 Polar Form of Complex Numbers
polar form of a conic10.5 Conic Sections in Polar Coordinates
polar grid8.3 Polar Coordinates, 8.3 Polar Coordinates
pole8.3 Polar Coordinates
polynomial3.6 Zeros of Polynomial Functions, 12.3 Continuity
polynomial function3.3 Power Functions and Polynomial Functions, 3.4 Graphs of Polynomial Functions, 3.4 Graphs of Polynomial Functions, 3.4 Graphs of Polynomial Functions
position vector8.8 Vectors, 8.8 Vectors
positive angle5.1 Angles, 5.1 Angles
power function3.3 Power Functions and Polynomial Functions
power rule for logarithms4.5 Logarithmic Properties, 4.5 Logarithmic Properties
probability11.7 Probability
probability model11.7 Probability
product of two matrices9.5 Matrices and Matrix Operations
product rule for logarithms4.5 Logarithmic Properties, 4.5 Logarithmic Properties
product-to-sum formulas7.4 Sum-to-Product and Product-to-Sum Formulas, 7.4 Sum-to-Product and Product-to-Sum Formulas
profit function9.1 Systems of Linear Equations: Two Variables
properties of determinants9.8 Solving Systems with Cramer's Rule
properties of limits12.2 Finding Limits: Properties of Limits
Proxima Centauri4.7 Exponential and Logarithmic Models
Pythagoras8.5 Polar Form of Complex Numbers
Pythagorean Identities7.1 Solving Trigonometric Equations with Identities, 7.1 Solving Trigonometric Equations with Identities
Pythagorean Identity5.2 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 Theorem7.3 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 angle5.2 Unit Circle: Sine and Cosine Functions
quadratic9.4 Partial Fractions, 9.4 Partial Fractions
quadratic equation7.5 Solving Trigonometric Equations
quadratic formula3.2 Quadratic Functions, 7.5 Solving Trigonometric Equations
quadratic function3.2 Quadratic Functions, 3.2 Quadratic Functions
quotient3.5 Dividing Polynomials
quotient identities7.1 Solving Trigonometric Equations with Identities, 7.1 Solving Trigonometric Equations with Identities
quotient rule for logarithms4.5 Logarithmic Properties
R
radian5.1 Angles, 5.1 Angles, 5.1 Angles
radian measure5.1 Angles, 5.1 Angles, 5.1 Angles
radical functions3.8 Inverses and Radical Functions
radiocarbon dating4.7 Exponential and Logarithmic Models
range1.1 Functions and Function Notation, 6.3 Inverse Trigonometric Functions
rate of change1.3 Rates of Change and Behavior of Graphs, 2.3 Modeling with Linear Functions
rational expression9.4 Partial Fractions, 9.4 Partial Fractions, 9.4 Partial Fractions
rational function3.7 Rational Functions, 3.7 Rational Functions, 3.7 Rational Functions, 12.2 Finding Limits: Properties of Limits
Rational Zero Theorem3.6 Zeros of Polynomial Functions, 3.6 Zeros of Polynomial Functions
ray5.1 Angles
reciprocal1.7 Inverse Functions, 3.3 Power Functions and Polynomial Functions
reciprocal function3.7 Rational Functions
reciprocal identities7.1 Solving Trigonometric Equations with Identities, 7.1 Solving Trigonometric Equations with Identities
reciprocal identity6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
rectangular coordinates8.3 Polar Coordinates, 8.3 Polar Coordinates, 8.3 Polar Coordinates
rectangular equation8.3 Polar Coordinates, 8.6 Parametric Equations
rectangular form8.5 Polar Form of Complex Numbers, 8.7 Parametric Equations: Graphs
recursive formula11.1 Sequences and Their Notations, 11.2 Arithmetic Sequences, 11.2 Arithmetic Sequences, 11.3 Geometric Sequences
reduction formulas7.3 Double-Angle, Half-Angle, and Reduction Formulas, 7.3 Double-Angle, Half-Angle, and Reduction Formulas
reference angle5.1 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
reflection4.2 Graphs of Exponential Functions, 4.4 Graphs of Logarithmic Functions
regression analysis4.8 Fitting Exponential Models to Data, 4.8 Fitting Exponential Models to Data, 4.8 Fitting Exponential Models to Data
relation1.1 Functions and Function Notation
remainder3.5 Dividing Polynomials
Remainder Theorem3.6 Zeros of Polynomial Functions
removable discontinuity3.7 Rational Functions, 3.7 Rational Functions, 12.3 Continuity
Restricting the domain1.7 Inverse Functions
resultant8.8 Vectors
revenue function9.1 Systems of Linear Equations: Two Variables
Richter Scale4.3 Logarithmic Functions
right triangle6.3 Inverse Trigonometric Functions
right triangles5.4 Right Triangle Trigonometry
right-hand limit12.1 Finding Limits: Numerical and Graphical Approaches, 12.3 Continuity
roots3.2 Quadratic Functions
rose curve8.4 Polar Coordinates: Graphs
row9.5 Matrices and Matrix Operations
row matrix9.5 Matrices and Matrix Operations
row operations9.6 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 form9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination, 9.6 Solving Systems with Gaussian Elimination
row-equivalent9.6 Solving Systems with Gaussian Elimination
S
sample space11.7 Probability
SAS (side-angle-side) triangle8.2 Non-right Triangles: Law of Cosines
scalar8.8 Vectors, 9.5 Matrices and Matrix Operations
scalar multiple8.8 Vectors, 9.5 Matrices and Matrix Operations
Scalar multiplication8.8 Vectors, 9.5 Matrices and Matrix Operations
scatter plot2.4 Fitting Linear Models to Data
secant5.3 The Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
secant function6.2 Graphs of the Other Trigonometric Functions
secant line12.4 Derivatives
sector of a circle5.1 Angles
sequence11.1 Sequences and Their Notations, 11.1 Sequences and Their Notations, 11.2 Arithmetic Sequences, 12.1 Finding Limits: Numerical and Graphical Approaches
series11.4 Series and Their Notations
set-builder notation1.2 Domain and Range
sigma11.4 Series and Their Notations
simple harmonic motion7.6 Modeling with Trigonometric Equations, 7.6 Modeling with Trigonometric Equations
sine7.1 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 function5.3 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
sine function 5.2 Unit Circle: Sine and Cosine Functions
sinusoidal function6.1 Graphs of the Sine and Cosine Functions, 7.6 Modeling with Trigonometric Equations
slope2.1 Linear Functions, 2.1 Linear Functions
slope of the curve12.4 Derivatives
slope of the tangent12.4 Derivatives
slope-intercept form2.1 Linear Functions
smooth curve3.3 Power Functions and Polynomial Functions
solution set9.2 Systems of Linear Equations: Three Variables
solving systems of linear equations9.1 Systems of Linear Equations: Two Variables
special angles5.2 Unit Circle: Sine and Cosine Functions, 5.4 Right Triangle Trigonometry, 7.2 Sum and Difference Identities
square matrix9.5 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) 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
stretch4.2 Graphs of Exponential Functions
stretching/compressing factor6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
substitution method9.1 Systems of Linear Equations: Two Variables
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
sum-to-product formulas7.4 Sum-to-Product and Product-to-Sum Formulas, 7.4 Sum-to-Product and Product-to-Sum Formulas
summation notation11.4 Series and Their Notations
surface area3.8 Inverses and Radical Functions
symmetry test8.4 Polar Coordinates: Graphs
synthetic division3.5 Dividing Polynomials, 3.6 Zeros of Polynomial Functions
system of equations9.6 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 equations2.3 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 equations9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of nonlinear inequalities9.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of three equations in three variables9.8 Solving Systems with Cramer's Rule
T
tangent5.3 The Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions, 6.2 Graphs of the Other Trigonometric Functions
tangent function6.2 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 line12.4 Derivatives
term11.1 Sequences and Their Notations, 11.2 Arithmetic Sequences
term of a polynomial function3.3 Power Functions and Polynomial Functions
terminal point8.8 Vectors, 8.8 Vectors
terminal side5.1 Angles
transformation1.5 Transformation of Functions
transformations2.2 Graphs of Linear Functions
translation10.1 The Ellipse
transverse axis10.2 The Hyperbola
trigonometric equations8.6 Parametric Equations
trigonometric functions5.4 Right Triangle Trigonometry
trigonometric identities8.2 Non-right Triangles: Law of Cosines
turning point3.3 Power Functions and Polynomial Functions, 3.4 Graphs of Polynomial Functions
two-sided limit12.1 Finding Limits: Numerical and Graphical Approaches, 12.4 Derivatives
U
union of two events11.7 Probability
unit circle5.1 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 vector8.8 Vectors
upper limit of summation11.4 Series and Their Notations
upper triangular form9.2 Systems of Linear Equations: Three Variables
V
varies directly3.9 Modeling Using Variation
varies inversely3.9 Modeling Using Variation
vector8.8 Vectors
vector addition8.8 Vectors
velocity12.4 Derivatives, 12.4 Derivatives
vertex3.2 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 function3.2 Quadratic Functions
vertical asymptote3.7 Rational Functions, 3.7 Rational Functions, 3.7 Rational Functions, 6.3 Inverse Trigonometric Functions
vertical compression1.5 Transformation of Functions
vertical line2.2 Graphs of Linear Functions
vertical line test1.1 Functions and Function Notation
vertical reflection1.5 Transformation of Functions
vertical shift1.5 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 stretch1.5 Transformation of Functions, 2.2 Graphs of Linear Functions, 4.4 Graphs of Logarithmic Functions
vertical tangent12.4 Derivatives
vertices10.1 The Ellipse, 10.1 The Ellipse
volume of a sphere3.3 Power Functions and Polynomial Functions
X
x-intercept2.2 Graphs of Linear Functions
Y
y-intercept2.1 Linear Functions, 2.2 Graphs of Linear Functions
Z
zeros3.2 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
Previous
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4.0 and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/precalculus/pages/1-introduction-to-functions
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/precalculus/pages/1-introduction-to-functions
Citation information

© Jan 21, 2021 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License 4.0 license. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.