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  1. Preface
  2. 1 Prerequisites
    1. Introduction to Prerequisites
    2. 1.1 Real Numbers: Algebra Essentials
    3. 1.2 Exponents and Scientific Notation
    4. 1.3 Radicals and Rational Exponents
    5. 1.4 Polynomials
    6. 1.5 Factoring Polynomials
    7. 1.6 Rational Expressions
    8. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Equations and Inequalities
    1. Introduction to Equations and Inequalities
    2. 2.1 The Rectangular Coordinate Systems and Graphs
    3. 2.2 Linear Equations in One Variable
    4. 2.3 Models and Applications
    5. 2.4 Complex Numbers
    6. 2.5 Quadratic Equations
    7. 2.6 Other Types of Equations
    8. 2.7 Linear Inequalities and Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Functions
    1. Introduction to Functions
    2. 3.1 Functions and Function Notation
    3. 3.2 Domain and Range
    4. 3.3 Rates of Change and Behavior of Graphs
    5. 3.4 Composition of Functions
    6. 3.5 Transformation of Functions
    7. 3.6 Absolute Value Functions
    8. 3.7 Inverse Functions
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Linear Functions
    1. Introduction to Linear Functions
    2. 4.1 Linear Functions
    3. 4.2 Modeling with Linear Functions
    4. 4.3 Fitting Linear Models to Data
    5. Chapter Review
      1. Key Terms
      2. Key Concepts
    6. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomial and Rational Functions
    1. Introduction to Polynomial and Rational Functions
    2. 5.1 Quadratic Functions
    3. 5.2 Power Functions and Polynomial Functions
    4. 5.3 Graphs of Polynomial Functions
    5. 5.4 Dividing Polynomials
    6. 5.5 Zeros of Polynomial Functions
    7. 5.6 Rational Functions
    8. 5.7 Inverses and Radical Functions
    9. 5.8 Modeling Using Variation
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Exponential and Logarithmic Functions
    1. Introduction to Exponential and Logarithmic Functions
    2. 6.1 Exponential Functions
    3. 6.2 Graphs of Exponential Functions
    4. 6.3 Logarithmic Functions
    5. 6.4 Graphs of Logarithmic Functions
    6. 6.5 Logarithmic Properties
    7. 6.6 Exponential and Logarithmic Equations
    8. 6.7 Exponential and Logarithmic Models
    9. 6.8 Fitting Exponential Models to Data
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 7.1 Systems of Linear Equations: Two Variables
    3. 7.2 Systems of Linear Equations: Three Variables
    4. 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 7.4 Partial Fractions
    6. 7.5 Matrices and Matrix Operations
    7. 7.6 Solving Systems with Gaussian Elimination
    8. 7.7 Solving Systems with Inverses
    9. 7.8 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
  9. 8 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 8.1 The Ellipse
    3. 8.2 The Hyperbola
    4. 8.3 The Parabola
    5. 8.4 Rotation of Axes
    6. 8.5 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
  10. 9 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 9.1 Sequences and Their Notations
    3. 9.2 Arithmetic Sequences
    4. 9.3 Geometric Sequences
    5. 9.4 Series and Their Notations
    6. 9.5 Counting Principles
    7. 9.6 Binomial Theorem
    8. 9.7 Probability
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  11. 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
  12. Index
A
absolute value function 3.2 Domain and Range
angle of rotation 8.4 Rotation of Axes
annual percentage rate (APR) 6.1 Exponential Functions
arithmetic series 9.4 Series and Their Notations
arrow notation 5.6 Rational Functions
associative property of addition 1.1 Real Numbers: Algebra Essentials
associative property of multiplication 1.1 Real Numbers: Algebra Essentials
asymptotes 8.2 The Hyperbola
axes of symmetry 8.2 The Hyperbola
C
center of a hyperbola 8.2 The Hyperbola
center of an ellipse 8.1 The Ellipse
central rectangle 8.2 The Hyperbola
co-vertex 8.1 The Ellipse
co-vertices 8.1 The Ellipse
combining functions 3.4 Composition of Functions
common logarithm 6.3 Logarithmic Functions
commutative property of addition 1.1 Real Numbers: Algebra Essentials
commutative property of multiplication 1.1 Real Numbers: Algebra Essentials
complement of an event 9.7 Probability
complex conjugate 2.4 Complex Numbers
Complex Conjugate Theorem 5.5 Zeros of Polynomial Functions
complex number 2.4 Complex Numbers
complex plane 2.4 Complex Numbers
composite function 3.4 Composition of Functions
composition of functions 3.4 Composition of Functions
compound interest 6.1 Exponential Functions
conic section 8.4 Rotation of Axes
constant function 3.2 Domain and Range
coordinate plane 8.3 The Parabola
Cornell Method 1.5 Factoring Polynomials
correlation coefficient 4.3 Fitting Linear Models to Data
D
decompose a composite function 3.4 Composition of Functions
decomposition 7.4 Partial Fractions
decreasing linear function 4.1 Linear Functions
degenerate conic sections 8.4 Rotation of Axes
degree of the polynomial equation 5.5 Zeros of Polynomial Functions
Descartes’ Rule of Signs 5.5 Zeros of Polynomial Functions
difference of squares 1.4 Polynomials
Disjoint events 9.5 Counting Principles
Distance Formula 8.2 The Hyperbola
distributive property 1.1 Real Numbers: Algebra Essentials
domain of a composite function 3.4 Composition of Functions
E
equation in quadratic form 2.6 Other Types of Equations
experiment 9.7 Probability
exponential function 6.1 Exponential Functions
extraneous solutions 2.6 Other Types of Equations
I
identity property of addition 1.1 Real Numbers: Algebra Essentials
identity property of multiplication 1.1 Real Numbers: Algebra Essentials
imaginary number 2.4 Complex Numbers
Imaginary numbers 2.4 Complex Numbers
inconsistent equation 2.2 Linear Equations in One Variable
increasing linear function 4.1 Linear Functions
index of summation 9.4 Series and Their Notations
infinite geometric sequence 9.4 Series and Their Notations
intersection 9.7 Probability
inverse of a radical function 5.7 Inverses and Radical Functions
inverse of a rational function 5.7 Inverses and Radical Functions
inverse property of addition 1.1 Real Numbers: Algebra Essentials
inverse property of multiplication 1.1 Real Numbers: Algebra Essentials
inverse variation 5.8 Modeling Using Variation
inverse variations 5.8 Modeling Using Variation
inversely proportional 5.8 Modeling Using Variation
invertible functions 5.7 Inverses and Radical Functions
L
least squares regression 4.3 Fitting Linear Models to Data
linear equation with three variables 7.2 Systems of Linear Equations: Three Variables
Linear functions 4.1 Linear Functions
Linear Regression Model 6.8 Fitting Exponential Models to Data
linear relationship 4.3 Fitting Linear Models to Data
long division 5.4 Dividing Polynomials
lower limit of summation 9.4 Series and Their Notations
M
major and minor axes 8.1 The Ellipse
maximum value 5.1 Quadratic Functions
minimum value 5.1 Quadratic Functions
minor axis 8.1 The Ellipse
mutually exclusive 9.5 Counting Principles
mutually exclusive events 9.7 Probability
P
partial fraction 7.4 Partial Fractions
partial fraction decomposition 7.4 Partial Fractions, 7.4 Partial Fractions
Pascal's Triangle 9.6 Binomial Theorem
Pascal’s Triangle 9.6 Binomial Theorem
perfect square trinomial 1.4 Polynomials
piecewise function 3.2 Domain and Range
piecewise functions 9.1 Sequences and Their Notations
point-slope form 4.1 Linear Functions
positive association 4.3 Fitting Linear Models to Data
probability 9.7 Probability
probability model 9.7 Probability, 9.7 Probability
probability of an event 9.7 Probability
product of two matrices 7.5 Matrices and Matrix Operations
Product Property 6.5 Logarithmic Properties
properties of determinants 7.8 Solving Systems with Cramer's Rule
R
radical equation 2.6 Other Types of Equations
reciprocal function 5.6 Rational Functions
Restricting the domain 3.7 Inverse Functions
roster notation 9.7 Probability
S
sample space 9.7 Probability
sample space S 9.7 Probability
scalar multiplication 7.5 Matrices and Matrix Operations
slope-intercept 4.1 Linear Functions
solving systems of linear equations 7.1 Systems of Linear Equations: Two Variables
square trinomial 8.1 The Ellipse
standard form of a quadratic function 5.1 Quadratic Functions
standard or graphing form 8.1 The Ellipse
summarizing the important concepts 1.5 Factoring Polynomials
system of three equations in three variables 7.8 Solving Systems with Cramer's Rule
U
union of two events 9.7 Probability
upper limit of summation 9.4 Series and Their Notations
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