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College Algebra with Corequisite Support

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College Algebra with Corequisite SupportIndex
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Table of contents
  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 maximum 3.3 Rates of Change and Behavior of Graphs
absolute minimum 3.3 Rates of Change and Behavior of Graphs
absolute value 3.2 Domain and Range, 3.6 Absolute Value Functions
absolute value equation 2.6 Other Types of Equations, 2.6 Other Types of Equations
absolute value function 3.2 Domain and Range
absolute value functions 3.6 Absolute Value Functions, 3.6 Absolute Value Functions
absolute value inequality 2.7 Linear Inequalities and Absolute Value Inequalities, 2.7 Linear Inequalities and Absolute Value Inequalities
addition method 7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables
Addition Principle 9.5 Counting Principles, 9.5 Counting Principles
addition property 2.7 Linear Inequalities and Absolute Value Inequalities
algebraic expression 1.1 Real Numbers: Algebra Essentials
angle of rotation 8.4 Rotation of Axes
annual interest 9.4 Series and Their Notations
annual percentage rate (APR) 6.1 Exponential Functions
annuity 9.4 Series and Their Notations
apoapsis 8.5 Conic Sections in Polar Coordinates
area 2.3 Models and Applications
area of a circle 5.2 Power Functions and Polynomial Functions
arithmetic sequence 9.2 Arithmetic Sequences, 9.2 Arithmetic Sequences, 9.2 Arithmetic Sequences, 9.2 Arithmetic Sequences, 9.2 Arithmetic Sequences, 9.4 Series and Their Notations
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
augmented matrix 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.7 Solving Systems with Inverses
augmented matrix form 7.6 Solving Systems with Gaussian Elimination
average rate of change 3.3 Rates of Change and Behavior of Graphs, 3.3 Rates of Change and Behavior of Graphs
axes of symmetry 8.2 The Hyperbola
axis of symmetry 5.1 Quadratic Functions, 5.1 Quadratic Functions, 8.3 The Parabola, 8.3 The Parabola
B
base 1.1 Real Numbers: Algebra Essentials
best fit 6.8 Fitting Exponential Models to Data
binomial 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.4 Dividing Polynomials
binomial coefficient 9.6 Binomial Theorem
binomial expansion 9.6 Binomial Theorem, 9.6 Binomial Theorem
Binomial Squares Pattern 8.1 The Ellipse
Binomial Theorem 9.6 Binomial Theorem
branch 8.2 The Hyperbola
break-even point 7.1 Systems of Linear Equations: Two Variables
C
carrying capacity 6.7 Exponential and Logarithmic Models
Cartesian coordinate system 2.1 The Rectangular Coordinate Systems and Graphs
Celsius 3.7 Inverse Functions
center 8.1 The Ellipse, 8.2 The Hyperbola
center of a hyperbola 8.2 The Hyperbola
center of an ellipse 8.1 The Ellipse
central rectangle 8.2 The Hyperbola
change-of-base formula 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
circle 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 8.1 The Ellipse
co-vertex 8.1 The Ellipse
co-vertices 8.1 The Ellipse
coefficient 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.2 Power Functions and Polynomial Functions, 5.5 Zeros of Polynomial Functions
coefficient matrix 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
column 7.5 Matrices and Matrix Operations
column matrix 7.5 Matrices and Matrix Operations
combinations 9.5 Counting Principles, 9.6 Binomial Theorem
combining functions 3.4 Composition of Functions
common base 6.6 Exponential and Logarithmic Equations
common difference 9.2 Arithmetic Sequences, 9.2 Arithmetic Sequences, 9.4 Series and Their Notations
common logarithm 6.3 Logarithmic Functions
common ratio 9.3 Geometric Sequences, 9.3 Geometric Sequences, 9.4 Series and Their Notations
commutative 3.4 Composition of 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
completing the square 2.5 Quadratic Equations, 2.5 Quadratic Equations, 8.1 The Ellipse
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 3.4 Composition of Functions, 3.7 Inverse Functions
composite function 3.4 Composition of Functions
composition of functions 3.4 Composition of Functions
compound inequality 2.7 Linear Inequalities and Absolute Value Inequalities
compound interest 6.1 Exponential Functions
compression 4.1 Linear Functions, 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions
conditional equation 2.2 Linear Equations in One Variable
conic 8.1 The Ellipse, 8.2 The Hyperbola, 8.5 Conic Sections in Polar Coordinates
conic section 8.4 Rotation of Axes
conjugate axis 8.2 The Hyperbola, 8.2 The Hyperbola
consistent system 7.1 Systems of Linear Equations: Two Variables
constant 1.1 Real Numbers: Algebra Essentials
constant function 3.2 Domain and Range
constant of variation 5.8 Modeling Using Variation, 5.8 Modeling Using Variation
continuous 5.3 Graphs of Polynomial Functions
continuous function 5.2 Power Functions and Polynomial Functions
coordinate plane 8.3 The Parabola
Cornell Method 1.5 Factoring Polynomials
correlation coefficient 4.3 Fitting Linear Models to Data
cost function 3.4 Composition of Functions, 7.1 Systems of Linear Equations: Two Variables
Cramer’s Rule 7.8 Solving Systems with Cramer's Rule, 7.8 Solving Systems with Cramer's Rule, 7.8 Solving Systems with Cramer's Rule, 7.8 Solving Systems with Cramer's Rule, 7.8 Solving Systems with Cramer's Rule
cube root 5.2 Power Functions and Polynomial Functions
cubic functions 5.7 Inverses and Radical Functions
cues 1.5 Factoring Polynomials
D
decompose a composite function 3.4 Composition of Functions
decomposition 7.4 Partial Fractions
decreasing function 3.3 Rates of Change and Behavior of Graphs, 4.1 Linear Functions
decreasing linear function 4.1 Linear Functions
degenerate conic sections 8.4 Rotation of Axes
degree 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.2 Power Functions and Polynomial Functions, 5.5 Zeros of Polynomial Functions
degree of the polynomial equation 5.5 Zeros of Polynomial Functions
dependent system 7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables, 7.2 Systems of Linear Equations: Three Variables
dependent variable 3.1 Functions and Function Notation, 6.1 Exponential Functions
Descartes’ Rule of Signs 5.5 Zeros of Polynomial Functions
determinant 7.7 Solving Systems with Inverses, 7.8 Solving Systems with Cramer's Rule, 7.8 Solving Systems with Cramer's Rule, 7.8 Solving Systems with Cramer's Rule
difference of squares 1.4 Polynomials
direct variation 5.8 Modeling Using Variation, 5.8 Modeling Using Variation
directrix 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates
discriminant 2.5 Quadratic Equations, 2.5 Quadratic Equations
Disjoint events 9.5 Counting Principles
distance formula 2.1 The Rectangular Coordinate Systems and Graphs, 8.2 The Hyperbola, 8.3 The Parabola
Distance Formula 8.2 The Hyperbola
distributive property 1.1 Real Numbers: Algebra Essentials
diverges 9.4 Series and Their Notations
dividend 5.4 Dividing Polynomials
Division Algorithm 5.4 Dividing Polynomials, 5.5 Zeros of Polynomial Functions
divisor 5.4 Dividing Polynomials
domain 3.1 Functions and Function Notation, 3.1 Functions and Function Notation, 3.1 Functions and Function Notation, 3.2 Domain and Range, 3.2 Domain and Range, 3.2 Domain and Range, 3.2 Domain and Range, 3.2 Domain and Range, 6.4 Graphs of Logarithmic Functions
domain and range 3.2 Domain and Range, 3.2 Domain and Range
domain of a composite function 3.4 Composition of Functions
doubling time 6.7 Exponential and Logarithmic Models
E
earthquake intensity 6.7 Exponential and Logarithmic Models
eccentricity 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates
electrostatic force 3.3 Rates of Change and Behavior of Graphs
element 7.5 Matrices and Matrix Operations
elimination 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
ellipse 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 8.1 The Ellipse, 8.1 The Ellipse, 8.1 The Ellipse, 8.1 The Ellipse, 8.1 The Ellipse, 8.3 The Parabola, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates
ellipsis 9.1 Sequences and Their Notations
end behavior 5.2 Power Functions and Polynomial Functions, 5.6 Rational Functions
endpoint 3.3 Rates of Change and Behavior of Graphs
entry 7.5 Matrices and Matrix Operations, 7.5 Matrices and Matrix Operations
equation 1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
equation in quadratic form 2.6 Other Types of Equations
equation in two variables 2.1 The Rectangular Coordinate Systems and Graphs
even function 3.5 Transformation of Functions
event 9.5 Counting Principles, 9.7 Probability
experiment 9.7 Probability
explicit formula 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.2 Arithmetic Sequences, 9.3 Geometric Sequences
exponent 1.1 Real Numbers: Algebra Essentials
Exponential decay 6.1 Exponential Functions, 6.1 Exponential Functions, 6.2 Graphs of Exponential Functions, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models, 6.8 Fitting Exponential Models to Data
exponential equation 6.6 Exponential and Logarithmic Equations
exponential equations 6.6 Exponential and Logarithmic Equations
exponential expression 5.2 Power Functions and Polynomial Functions
exponential function 6.1 Exponential Functions
exponential growth 6.1 Exponential Functions, 6.1 Exponential Functions, 6.2 Graphs of Exponential Functions, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models, 6.7 Exponential and Logarithmic Models
exponential notation 1.1 Real Numbers: Algebra Essentials
extraneous solution 6.6 Exponential and Logarithmic Equations
extraneous solutions 2.6 Other Types of Equations
extrapolation 4.3 Fitting Linear Models to Data
F
factor by grouping 1.5 Factoring Polynomials
Factor Theorem 5.5 Zeros of Polynomial Functions
factorial 9.1 Sequences and Their Notations
factoring 2.5 Quadratic Equations
Fahrenheit 3.7 Inverse Functions
feasible region 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
finite arithmetic sequence 9.2 Arithmetic Sequences
finite sequence 9.1 Sequences and Their Notations
fixed mindset 1.4 Polynomials
foci 8.1 The Ellipse, 8.1 The Ellipse, 8.1 The Ellipse, 8.2 The Hyperbola
focus 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 8.1 The Ellipse, 8.2 The Hyperbola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates
FOIL 1.4 Polynomials
formula 1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
function 3.1 Functions and Function Notation, 3.1 Functions and Function Notation, 3.2 Domain and Range, 3.2 Domain and Range, 3.4 Composition of Functions, 3.7 Inverse Functions, 4.1 Linear Functions, 9.1 Sequences and Their Notations
function notation 3.1 Functions and Function Notation
Fundamental Counting Principle 9.5 Counting Principles
Fundamental Theorem of Algebra 5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
G
Gauss 7.2 Systems of Linear Equations: Three Variables, 7.6 Solving Systems with Gaussian Elimination
Gaussian elimination 7.2 Systems of Linear Equations: Three Variables, 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination
general form 5.1 Quadratic Functions, 5.1 Quadratic Functions
general form of a quadratic function 5.1 Quadratic Functions
general form of the equation of a circle 8.1 The Ellipse
general term 9.1 Sequences and Their Notations
geometric sequence 9.3 Geometric Sequences, 9.3 Geometric Sequences, 9.4 Series and Their Notations
geometric series 9.4 Series and Their Notations
global maximum 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
global minimum 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
graph in two variables 2.1 The Rectangular Coordinate Systems and Graphs
graphing 3.2 Domain and Range
greatest common factor 1.5 Factoring Polynomials, 1.5 Factoring Polynomials, 2.5 Quadratic Equations
growth mindset 1.4 Polynomials
H
half-life 6.6 Exponential and Logarithmic Equations, 6.7 Exponential and Logarithmic Models
heading 1.5 Factoring Polynomials
Heaviside method 7.4 Partial Fractions
horizontal asymptote 5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions
horizontal compression 3.5 Transformation of Functions
horizontal line 2.2 Linear Equations in One Variable, 4.1 Linear Functions, 4.1 Linear Functions
horizontal line test 3.1 Functions and Function Notation, 3.7 Inverse Functions
horizontal reflection 3.5 Transformation of Functions
horizontal shift 3.5 Transformation of Functions, 6.2 Graphs of Exponential Functions, 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions
horizontal stretch 3.5 Transformation of Functions
hyperbola 8.2 The Hyperbola, 8.2 The Hyperbola, 8.2 The Hyperbola, 8.2 The Hyperbola, 8.2 The Hyperbola, 8.2 The Hyperbola, 8.2 The Hyperbola, 8.2 The Hyperbola, 8.2 The Hyperbola, 8.3 The Parabola, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates
I
icons 1.5 Factoring Polynomials
identity equation 2.2 Linear Equations in One Variable
identity matrix 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
identity property of addition 1.1 Real Numbers: Algebra Essentials
identity property of multiplication 1.1 Real Numbers: Algebra Essentials
illustrations 1.5 Factoring Polynomials
imaginary number 2.4 Complex Numbers
Imaginary numbers 2.4 Complex Numbers
inconsistent equation 2.2 Linear Equations in One Variable
inconsistent system 7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables, 7.2 Systems of Linear Equations: Three Variables
increasing function 3.3 Rates of Change and Behavior of Graphs, 4.1 Linear Functions
increasing linear function 4.1 Linear Functions
independent system 7.1 Systems of Linear Equations: Two Variables
independent variable 3.1 Functions and Function Notation, 6.1 Exponential Functions
index 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
index of summation 9.4 Series and Their Notations
inequality 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
infinite geometric sequence 9.4 Series and Their Notations
infinite sequence 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations
infinite series 9.4 Series and Their Notations
input 3.1 Functions and Function Notation
integers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
intercepts 2.1 The Rectangular Coordinate Systems and Graphs
Intermediate Value Theorem 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
interpolation 4.3 Fitting Linear Models to Data
intersection 9.7 Probability
interval 2.7 Linear Inequalities and Absolute Value Inequalities
interval notation 2.7 Linear Inequalities and Absolute Value Inequalities, 3.2 Domain and Range, 3.2 Domain and Range, 3.3 Rates of Change and Behavior of Graphs
inverse function 3.7 Inverse Functions, 5.7 Inverses and Radical Functions
inverse matrix 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
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
inverses 3.7 Inverse Functions
invertible functions 5.7 Inverses and Radical Functions
invertible matrix 7.7 Solving Systems with Inverses, 7.8 Solving Systems with Cramer's Rule
irrational numbers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
J
joint variation 5.8 Modeling Using Variation
K
knowledge space 1.3 Radicals and Rational Exponents
L
latus rectum 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola
leading coefficient 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.5 Zeros of Polynomial Functions
leading term 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions
learning sciences 1.3 Radicals and Rational Exponents
least common denominator 1.6 Rational Expressions, 2.2 Linear Equations in One Variable
least squares regression 4.3 Fitting Linear Models to Data
left column 1.5 Factoring Polynomials
linchpin topics 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
linear 4.3 Fitting Linear Models to Data
linear equation 2.2 Linear Equations in One Variable
linear equation with three variables 7.2 Systems of Linear Equations: Three Variables
Linear Factorization Theorem 5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
linear function 4.1 Linear Functions, 4.1 Linear Functions
Linear functions 4.1 Linear Functions
linear growth 6.1 Exponential Functions
linear model 4.2 Modeling with Linear Functions, 4.3 Fitting Linear Models to Data
Linear Regression Model 6.8 Fitting Exponential Models to Data
linear relationship 4.3 Fitting Linear Models to Data
local extrema 3.3 Rates of Change and Behavior of Graphs
local maximum 3.3 Rates of Change and Behavior of Graphs, 5.3 Graphs of Polynomial Functions
local minimum 3.3 Rates of Change and Behavior of Graphs, 5.3 Graphs of Polynomial Functions
logarithm 6.3 Logarithmic Functions
logarithmic equation 6.6 Exponential and Logarithmic Equations
Logarithmic Function 6.7 Exponential and Logarithmic Models
logarithmic model 6.8 Fitting Exponential Models to Data
logistic growth model 6.7 Exponential and Logarithmic Models
long division 5.4 Dividing Polynomials
lower limit of summation 9.4 Series and Their Notations
M
magnitude 3.2 Domain and Range, 3.5 Transformation of Functions
main diagonal 7.6 Solving Systems with Gaussian Elimination
major and minor axes 8.1 The Ellipse
major axis 8.1 The Ellipse, 8.1 The Ellipse
matrix 7.5 Matrices and Matrix Operations, 7.5 Matrices and Matrix Operations, 7.5 Matrices and Matrix Operations, 7.6 Solving Systems with Gaussian Elimination
matrix multiplication 7.5 Matrices and Matrix Operations, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
matrix operations 7.5 Matrices and Matrix Operations
maximum value 5.1 Quadratic Functions
midpoint formula 2.1 The Rectangular Coordinate Systems and Graphs
mind map 1.5 Factoring Polynomials
minimum value 5.1 Quadratic Functions
minor axis 8.1 The Ellipse
minor of an entry 7.7 Solving Systems with Inverses
model breakdown 4.3 Fitting Linear Models to Data
modulus 3.2 Domain and Range
monomial 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions
Multiplication Principle 9.5 Counting Principles, 9.5 Counting Principles
multiplication property 2.7 Linear Inequalities and Absolute Value Inequalities
multiplicative inverse 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
multiplicative inverse of a matrix 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
multiplicity 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
mutually exclusive 9.5 Counting Principles
mutually exclusive events 9.7 Probability
N
n factorial 9.1 Sequences and Their Notations
natural exponential function 6.1 Exponential Functions
natural logarithm 6.3 Logarithmic Functions, 6.6 Exponential and Logarithmic Equations
natural numbers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
negative association 4.3 Fitting Linear Models to Data
Newton’s Law of Cooling 6.7 Exponential and Logarithmic Models
nominal rate 6.1 Exponential Functions
nondegenerate conic sections 8.4 Rotation of Axes
nonlinear inequality 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
notes during class 1.5 Factoring Polynomials
Notice 8.2 The Hyperbola
nth partial sum 9.4 Series and Their Notations
nth term of the sequence 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations
O
odd function 3.5 Transformation of Functions
one-to-one 6.2 Graphs of Exponential Functions, 6.3 Logarithmic Functions, 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
one-to-one function 3.1 Functions and Function Notation, 3.7 Inverse Functions, 3.7 Inverse Functions
order of magnitude 6.7 Exponential and Logarithmic Models
order of operations 1.1 Real Numbers: Algebra Essentials
ordered pair 2.1 The Rectangular Coordinate Systems and Graphs, 3.1 Functions and Function Notation, 3.2 Domain and Range
ordered triple 7.2 Systems of Linear Equations: Three Variables, 7.2 Systems of Linear Equations: Three Variables
origin 2.1 The Rectangular Coordinate Systems and Graphs, 3.6 Absolute Value Functions
outcome 9.5 Counting Principles
outcomes 9.7 Probability
output 3.1 Functions and Function Notation
P
parabola 5.1 Quadratic Functions, 5.1 Quadratic Functions, 5.1 Quadratic Functions, 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates
parallel 2.2 Linear Equations in One Variable
parallel lines 4.1 Linear Functions, 4.1 Linear Functions
parent function 6.4 Graphs of Logarithmic Functions
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
periapsis 8.5 Conic Sections in Polar Coordinates
perimeter 2.3 Models and Applications
permutation 9.5 Counting Principles
perpendicular 2.2 Linear Equations in One Variable
perpendicular lines 4.1 Linear Functions, 4.1 Linear Functions
pH 6.5 Logarithmic Properties
piecewise function 3.2 Domain and Range
piecewise functions 9.1 Sequences and Their Notations
plane 7.2 Systems of Linear Equations: Three Variables
point-slope form 4.1 Linear Functions
point-slope formula 2.2 Linear Equations in One Variable, 8.2 The Hyperbola
polar equation 8.5 Conic Sections in Polar Coordinates
polar form of a conic 8.5 Conic Sections in Polar Coordinates
polynomial 1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.5 Zeros of Polynomial Functions
polynomial equation 2.6 Other Types of Equations, 5.5 Zeros of Polynomial Functions
polynomial function 5.2 Power Functions and Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
positive association 4.3 Fitting Linear Models to Data
power function 5.2 Power Functions and Polynomial Functions, 5.2 Power Functions and Polynomial Functions
Power Property 6.5 Logarithmic Properties
power rule for logarithms 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
principal nth root 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
principal square root 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
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
product rule for logarithms 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
profit function 7.1 Systems of Linear Equations: Two Variables
properties of determinants 7.8 Solving Systems with Cramer's Rule
Proxima Centauri 6.7 Exponential and Logarithmic Models
Pythagorean Theorem 2.1 The Rectangular Coordinate Systems and Graphs, 2.5 Quadratic Equations
Q
quadrant 2.1 The Rectangular Coordinate Systems and Graphs
quadratic 7.4 Partial Fractions, 7.4 Partial Fractions
quadratic equation 2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations
quadratic formula 2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations
quadratic function 5.1 Quadratic Functions, 5.1 Quadratic Functions, 5.1 Quadratic Functions, 5.1 Quadratic Functions
quotient 5.4 Dividing Polynomials
Quotient Property 6.5 Logarithmic Properties
quotient rule for logarithms 6.5 Logarithmic Properties
R
radical 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
radical equation 2.6 Other Types of Equations
radical expression 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
Radical expressions 1.3 Radicals and Rational Exponents
radical functions 5.7 Inverses and Radical Functions
radicand 1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents, 2.6 Other Types of Equations
radiocarbon dating 6.7 Exponential and Logarithmic Models
radius 8.1 The Ellipse
range 3.1 Functions and Function Notation, 3.1 Functions and Function Notation, 3.2 Domain and Range, 6.4 Graphs of Logarithmic Functions
rate of change 3.3 Rates of Change and Behavior of Graphs, 4.2 Modeling with Linear Functions
rational equation 2.2 Linear Equations in One Variable
rational expression 1.6 Rational Expressions, 2.2 Linear Equations in One Variable, 7.4 Partial Fractions, 7.4 Partial Fractions, 7.4 Partial Fractions
rational function 5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions
rational number 2.2 Linear Equations in One Variable
rational numbers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
Rational Zero Theorem 5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
real number line 1.1 Real Numbers: Algebra Essentials
real numbers 1.1 Real Numbers: Algebra Essentials
reciprocal 2.2 Linear Equations in One Variable, 3.7 Inverse Functions, 5.2 Power Functions and Polynomial Functions
reciprocal function 5.6 Rational Functions
recursive formula 9.1 Sequences and Their Notations, 9.2 Arithmetic Sequences, 9.2 Arithmetic Sequences, 9.3 Geometric Sequences
Reflect 1.5 Factoring Polynomials
reflection 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions
regression analysis 6.8 Fitting Exponential Models to Data, 6.8 Fitting Exponential Models to Data, 6.8 Fitting Exponential Models to Data
regression line 4.3 Fitting Linear Models to Data
relation 3.1 Functions and Function Notation, 3.1 Functions and Function Notation, 3.2 Domain and Range
remainder 5.4 Dividing Polynomials
Remainder Theorem 5.5 Zeros of Polynomial Functions
removable discontinuity 5.6 Rational Functions, 5.6 Rational Functions
Restricting the domain 3.7 Inverse Functions
revenue function 7.1 Systems of Linear Equations: Two Variables
Richter Scale 6.3 Logarithmic Functions
right section 1.5 Factoring Polynomials
roots 5.1 Quadratic Functions
roster notation 9.7 Probability
row 7.5 Matrices and Matrix Operations
row matrix 7.5 Matrices and Matrix Operations
row operations 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
row-echelon form 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination
row-equivalent 7.6 Solving Systems with Gaussian Elimination
S
sample space 9.7 Probability
sample space S 9.7 Probability
scalar 7.5 Matrices and Matrix Operations
scalar multiple 7.5 Matrices and Matrix Operations, 7.5 Matrices and Matrix Operations
scalar multiplication 7.5 Matrices and Matrix Operations
scatter plot 4.3 Fitting Linear Models to Data
Scatter Plot 6.8 Fitting Exponential Models to Data
scatterplot 4.3 Fitting Linear Models to Data
scientific notation 1.2 Exponents and Scientific Notation, 1.2 Exponents and Scientific Notation, 1.2 Exponents and Scientific Notation
sequence 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.2 Arithmetic Sequences
series 9.4 Series and Their Notations, 9.4 Series and Their Notations
set-builder notation 2.7 Linear Inequalities and Absolute Value Inequalities, 3.2 Domain and Range
sigma 9.4 Series and Their Notations
slope 2.2 Linear Equations in One Variable, 3.3 Rates of Change and Behavior of Graphs, 4.1 Linear Functions
slope-intercept 4.1 Linear Functions
slope-intercept form 4.1 Linear Functions, 4.1 Linear Functions, 4.1 Linear Functions
smooth curve 5.2 Power Functions and Polynomial Functions
solution set 2.2 Linear Equations in One Variable, 7.2 Systems of Linear Equations: Three Variables
Solutions 7.2 Systems of Linear Equations: Three Variables
solving systems of linear equations 7.1 Systems of Linear Equations: Two Variables
square matrix 7.5 Matrices and Matrix Operations, 7.7 Solving Systems with Inverses, 7.8 Solving Systems with Cramer's Rule
square root property 2.5 Quadratic Equations, 8.1 The Ellipse
square trinomial 8.1 The Ellipse
standard form 2.2 Linear Equations in One Variable
standard form of a quadratic function 5.1 Quadratic Functions
standard or graphing form 8.1 The Ellipse
stretch 6.2 Graphs of Exponential Functions
subsets 1.3 Radicals and Rational Exponents
substitution method 7.1 Systems of Linear Equations: Two Variables
summarizing the important concepts 1.5 Factoring Polynomials
summary 1.5 Factoring Polynomials
summation notation 9.4 Series and Their Notations, 9.4 Series and Their Notations
surface area 5.7 Inverses and Radical Functions
symmetric 5.1 Quadratic Functions
synthetic division 5.4 Dividing Polynomials, 5.5 Zeros of Polynomial Functions
system of equations 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.7 Solving Systems with Inverses
system of linear equations 4.2 Modeling with Linear Functions, 7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables
system of nonlinear equations 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of nonlinear inequalities 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of three equations in three variables 7.8 Solving Systems with Cramer's Rule
T
term 5.2 Power Functions and Polynomial Functions, 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.2 Arithmetic Sequences
term of a polynomial 1.4 Polynomials, 1.4 Polynomials
term of a polynomial function 5.2 Power Functions and Polynomial Functions
test questions 1.5 Factoring Polynomials
The loudness level, D 6.7 Exponential and Logarithmic Models
transformation 3.5 Transformation of Functions, 4.1 Linear Functions
transformations 3.5 Transformation of Functions
translation 8.1 The Ellipse
transverse axis 8.2 The Hyperbola, 8.2 The Hyperbola
trinomial 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions
turning point 5.2 Power Functions and Polynomial Functions, 5.3 Graphs of Polynomial Functions
U
union of two events 9.7 Probability
upper limit of summation 9.4 Series and Their Notations
upper triangular form 7.2 Systems of Linear Equations: Three Variables
V
variable 1.1 Real Numbers: Algebra Essentials
varies directly 5.8 Modeling Using Variation, 5.8 Modeling Using Variation
varies inversely 5.8 Modeling Using Variation
vertex 5.1 Quadratic Functions, 5.1 Quadratic Functions, 8.1 The Ellipse, 8.1 The Ellipse, 8.2 The Hyperbola, 8.3 The Parabola, 8.3 The Parabola
vertex form of a quadratic function 5.1 Quadratic Functions
vertical asymptote 5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions
vertical compression 3.5 Transformation of Functions
vertical line 2.2 Linear Equations in One Variable, 4.1 Linear Functions, 4.1 Linear Functions
vertical line test 3.1 Functions and Function Notation, 3.7 Inverse Functions
vertical reflection 3.5 Transformation of Functions
vertical shift 3.5 Transformation of Functions, 4.1 Linear Functions, 6.2 Graphs of Exponential Functions, 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions, 6.7 Exponential and Logarithmic Models
vertical stretch 3.5 Transformation of Functions, 4.1 Linear Functions, 6.4 Graphs of Logarithmic Functions
vertices 8.1 The Ellipse, 8.1 The Ellipse
volume 2.3 Models and Applications
volume of a sphere 5.2 Power Functions and Polynomial Functions
W
whole numbers 1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
X
x-axis 2.1 The Rectangular Coordinate Systems and Graphs
x-coordinate 2.1 The Rectangular Coordinate Systems and Graphs
x-intercept 2.1 The Rectangular Coordinate Systems and Graphs, 4.1 Linear Functions
x x -intercept 5.6 Rational Functions
Y
y-axis 2.1 The Rectangular Coordinate Systems and Graphs
y-coordinate 2.1 The Rectangular Coordinate Systems and Graphs
y-intercept 2.1 The Rectangular Coordinate Systems and Graphs, 4.1 Linear Functions
y y -intercept 5.6 Rational Functions
Z
Zero Product Property 5.3 Graphs of Polynomial Functions
zero-product property 2.5 Quadratic Equations
zeros 5.1 Quadratic Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.5 Zeros of Polynomial Functions
Zeros of the Function 5.5 Zeros of Polynomial Functions
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