Skip to Content
OpenStax Logo
College Algebra with Corequisite Support

Index

College Algebra with Corequisite SupportIndex
  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 maximum3.3 Rates of Change and Behavior of Graphs
absolute minimum3.3 Rates of Change and Behavior of Graphs
absolute value3.2 Domain and Range, 3.6 Absolute Value Functions
absolute value equation2.6 Other Types of Equations, 2.6 Other Types of Equations
absolute value function3.2 Domain and Range
absolute value functions3.6 Absolute Value Functions, 3.6 Absolute Value Functions
absolute value inequality2.7 Linear Inequalities and Absolute Value Inequalities, 2.7 Linear Inequalities and Absolute Value Inequalities
addition method7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables
Addition Principle9.5 Counting Principles
Addition Principle 9.5 Counting Principles
addition property2.7 Linear Inequalities and Absolute Value Inequalities
algebraic expression1.1 Real Numbers: Algebra Essentials
angle of rotation8.4 Rotation of Axes
annual interest9.4 Series and Their Notations
annual percentage rate (APR)6.1 Exponential Functions
annuity9.4 Series and Their Notations
apoapsis8.5 Conic Sections in Polar Coordinates
area2.3 Models and Applications
area of a circle5.2 Power Functions and Polynomial Functions
arithmetic sequence9.2 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 series9.4 Series and Their Notations
arrow notation5.6 Rational Functions
associative property of addition1.1 Real Numbers: Algebra Essentials
associative property of multiplication1.1 Real Numbers: Algebra Essentials
asymptotes8.2 The Hyperbola
augmented matrix7.6 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 form7.6 Solving Systems with Gaussian Elimination
average rate of change3.3 Rates of Change and Behavior of Graphs, 3.3 Rates of Change and Behavior of Graphs
axes of symmetry8.2 The Hyperbola
axis of symmetry5.1 Quadratic Functions, 5.1 Quadratic Functions, 8.3 The Parabola, 8.3 The Parabola
B
base1.1 Real Numbers: Algebra Essentials
best fit6.8 Fitting Exponential Models to Data
binomial1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.4 Dividing Polynomials
binomial coefficient 9.6 Binomial Theorem
binomial expansion9.6 Binomial Theorem, 9.6 Binomial Theorem
Binomial Squares Pattern8.1 The Ellipse
Binomial Theorem9.6 Binomial Theorem
branch8.2 The Hyperbola
break-even point7.1 Systems of Linear Equations: Two Variables
C
carrying capacity6.7 Exponential and Logarithmic Models
Cartesian coordinate system2.1 The Rectangular Coordinate Systems and Graphs
Celsius3.7 Inverse Functions
center8.1 The Ellipse, 8.2 The Hyperbola
center of a hyperbola8.2 The Hyperbola
center of an ellipse8.1 The Ellipse
central rectangle8.2 The Hyperbola
change-of-base formula6.5 Logarithmic Properties, 6.5 Logarithmic Properties
circle7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables, 8.1 The Ellipse
co-vertex8.1 The Ellipse
co-vertices8.1 The Ellipse
coefficient1.4 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 matrix7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
column7.5 Matrices and Matrix Operations
column matrix7.5 Matrices and Matrix Operations
combinations9.5 Counting Principles, 9.6 Binomial Theorem
combining functions3.4 Composition of Functions
common base6.6 Exponential and Logarithmic Equations
common difference9.2 Arithmetic Sequences, 9.2 Arithmetic Sequences, 9.4 Series and Their Notations
common logarithm6.3 Logarithmic Functions
common ratio9.3 Geometric Sequences, 9.3 Geometric Sequences, 9.4 Series and Their Notations
commutative3.4 Composition of Functions
commutative property of addition1.1 Real Numbers: Algebra Essentials
commutative property of multiplication1.1 Real Numbers: Algebra Essentials
complement of an event 9.7 Probability
completing the square2.5 Quadratic Equations, 2.5 Quadratic Equations, 8.1 The Ellipse
complex conjugate2.4 Complex Numbers
Complex Conjugate Theorem5.5 Zeros of Polynomial Functions
complex number2.4 Complex Numbers
complex plane2.4 Complex Numbers
composite3.4 Composition of Functions, 3.7 Inverse Functions
composite function3.4 Composition of Functions
composition of functions3.4 Composition of Functions
compound inequality2.7 Linear Inequalities and Absolute Value Inequalities
compound interest6.1 Exponential Functions
compression4.1 Linear Functions, 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions
conditional equation2.2 Linear Equations in One Variable
conic8.1 The Ellipse, 8.2 The Hyperbola, 8.5 Conic Sections in Polar Coordinates
conic section8.4 Rotation of Axes
conjugate axis8.2 The Hyperbola, 8.2 The Hyperbola
consistent system7.1 Systems of Linear Equations: Two Variables
constant1.1 Real Numbers: Algebra Essentials
constant function3.2 Domain and Range
constant of variation5.8 Modeling Using Variation, 5.8 Modeling Using Variation
continuous5.3 Graphs of Polynomial Functions
continuous function5.2 Power Functions and Polynomial Functions
coordinate plane8.3 The Parabola
Cornell Method1.5 Factoring Polynomials
correlation coefficient4.3 Fitting Linear Models to Data
cost function3.4 Composition of Functions, 7.1 Systems of Linear Equations: Two Variables
Cramer’s Rule7.8 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 root5.2 Power Functions and Polynomial Functions
cubic functions5.7 Inverses and Radical Functions
cues1.5 Factoring Polynomials
D
decompose a composite function3.4 Composition of Functions
decomposition7.4 Partial Fractions
decreasing function3.3 Rates of Change and Behavior of Graphs, 4.1 Linear Functions
decreasing linear function4.1 Linear Functions
degenerate conic sections8.4 Rotation of Axes
degree1.4 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 equation5.5 Zeros of Polynomial Functions
dependent system7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables, 7.2 Systems of Linear Equations: Three Variables
dependent variable3.1 Functions and Function Notation, 6.1 Exponential Functions
Descartes’ Rule of Signs5.5 Zeros of Polynomial Functions
determinant7.7 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 squares1.4 Polynomials
direct variation5.8 Modeling Using Variation, 5.8 Modeling Using Variation
directrix7.3 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
discriminant2.5 Quadratic Equations, 2.5 Quadratic Equations
Disjoint events9.5 Counting Principles
distance formula2.1 The Rectangular Coordinate Systems and Graphs, 8.2 The Hyperbola, 8.2 The Hyperbola, 8.3 The Parabola
distributive property1.1 Real Numbers: Algebra Essentials
diverges9.4 Series and Their Notations
dividend5.4 Dividing Polynomials
Division Algorithm5.4 Dividing Polynomials, 5.5 Zeros of Polynomial Functions
divisor5.4 Dividing Polynomials
domain3.1 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 range3.2 Domain and Range, 3.2 Domain and Range
domain of a composite function3.4 Composition of Functions
doubling time6.7 Exponential and Logarithmic Models
E
earthquake intensity6.7 Exponential and Logarithmic Models
eccentricity8.5 Conic Sections in Polar Coordinates, 8.5 Conic Sections in Polar Coordinates
electrostatic force3.3 Rates of Change and Behavior of Graphs
element7.5 Matrices and Matrix Operations
elimination7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
ellipse7.3 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
ellipsis9.1 Sequences and Their Notations
end behavior5.2 Power Functions and Polynomial Functions, 5.6 Rational Functions
endpoint3.3 Rates of Change and Behavior of Graphs
entry7.5 Matrices and Matrix Operations, 7.5 Matrices and Matrix Operations
equation1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
equation in quadratic form2.6 Other Types of Equations
equation in two variables2.1 The Rectangular Coordinate Systems and Graphs
even function3.5 Transformation of Functions
event9.5 Counting Principles, 9.7 Probability
experiment9.7 Probability
explicit formula9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.2 Arithmetic Sequences, 9.3 Geometric Sequences
exponent1.1 Real Numbers: Algebra Essentials
Exponential decay6.1 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 equation6.6 Exponential and Logarithmic Equations
exponential equations6.6 Exponential and Logarithmic Equations
exponential expression5.2 Power Functions and Polynomial Functions
exponential function6.1 Exponential Functions
exponential growth6.1 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 notation1.1 Real Numbers: Algebra Essentials
extraneous solution6.6 Exponential and Logarithmic Equations
extraneous solutions2.6 Other Types of Equations
extrapolation4.3 Fitting Linear Models to Data
F
factor by grouping1.5 Factoring Polynomials
Factor Theorem5.5 Zeros of Polynomial Functions
factorial9.1 Sequences and Their Notations
factoring2.5 Quadratic Equations
Fahrenheit3.7 Inverse Functions
feasible region7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
finite arithmetic sequence9.2 Arithmetic Sequences
finite sequence9.1 Sequences and Their Notations
fixed mindset1.4 Polynomials
foci8.1 The Ellipse, 8.1 The Ellipse, 8.1 The Ellipse, 8.2 The Hyperbola
focus7.3 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
FOIL1.4 Polynomials
formula1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
function3.1 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 notation3.1 Functions and Function Notation
Fundamental Counting Principle9.5 Counting Principles
Fundamental Theorem of Algebra5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
G
Gauss7.2 Systems of Linear Equations: Three Variables, 7.6 Solving Systems with Gaussian Elimination
Gaussian elimination7.2 Systems of Linear Equations: Three Variables, 7.6 Solving Systems with Gaussian Elimination, 7.6 Solving Systems with Gaussian Elimination
general form5.1 Quadratic Functions, 5.1 Quadratic Functions
general form of a quadratic function5.1 Quadratic Functions
general form of the equation of a circle8.1 The Ellipse
general term9.1 Sequences and Their Notations
geometric sequence9.3 Geometric Sequences, 9.3 Geometric Sequences, 9.4 Series and Their Notations
geometric series9.4 Series and Their Notations
global maximum5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
global minimum5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
graph in two variables2.1 The Rectangular Coordinate Systems and Graphs
graphing3.2 Domain and Range
greatest common factor1.5 Factoring Polynomials, 1.5 Factoring Polynomials, 2.5 Quadratic Equations
growth mindset1.4 Polynomials
H
half-life6.6 Exponential and Logarithmic Equations, 6.7 Exponential and Logarithmic Models
heading1.5 Factoring Polynomials
Heaviside method7.4 Partial Fractions
horizontal asymptote5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions
horizontal compression3.5 Transformation of Functions
horizontal line2.2 Linear Equations in One Variable, 4.1 Linear Functions, 4.1 Linear Functions
horizontal line test3.1 Functions and Function Notation, 3.7 Inverse Functions
horizontal reflection3.5 Transformation of Functions
horizontal shift3.5 Transformation of Functions, 6.2 Graphs of Exponential Functions, 6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions
horizontal stretch3.5 Transformation of Functions
hyperbola8.2 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
icons1.5 Factoring Polynomials
identity equation2.2 Linear Equations in One Variable
identity matrix7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
identity property of addition1.1 Real Numbers: Algebra Essentials
identity property of multiplication1.1 Real Numbers: Algebra Essentials
illustrations1.5 Factoring Polynomials
imaginary number2.4 Complex Numbers
Imaginary numbers2.4 Complex Numbers
inconsistent equation2.2 Linear Equations in One Variable
inconsistent system7.1 Systems of Linear Equations: Two Variables, 7.1 Systems of Linear Equations: Two Variables, 7.2 Systems of Linear Equations: Three Variables
increasing function3.3 Rates of Change and Behavior of Graphs, 4.1 Linear Functions
increasing linear function4.1 Linear Functions
independent system7.1 Systems of Linear Equations: Two Variables
independent variable3.1 Functions and Function Notation, 6.1 Exponential Functions
index1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
index of summation9.4 Series and Their Notations
inequality7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
infinite geometric sequence9.4 Series and Their Notations
infinite sequence9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations
infinite series9.4 Series and Their Notations
input3.1 Functions and Function Notation
integers1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
intercepts2.1 The Rectangular Coordinate Systems and Graphs
Intermediate Value Theorem5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
interpolation4.3 Fitting Linear Models to Data
intersection9.7 Probability
interval2.7 Linear Inequalities and Absolute Value Inequalities
interval notation2.7 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 function3.7 Inverse Functions, 5.7 Inverses and Radical Functions
inverse matrix7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
inverse of a radical function5.7 Inverses and Radical Functions
inverse of a rational function5.7 Inverses and Radical Functions
inverse property of addition1.1 Real Numbers: Algebra Essentials
inverse property of multiplication1.1 Real Numbers: Algebra Essentials
inverse variation5.8 Modeling Using Variation
inverse variations5.8 Modeling Using Variation
inversely proportional5.8 Modeling Using Variation
inverses3.7 Inverse Functions
invertible functions5.7 Inverses and Radical Functions
invertible matrix7.7 Solving Systems with Inverses, 7.8 Solving Systems with Cramer's Rule
irrational numbers1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
J
joint variation5.8 Modeling Using Variation
K
knowledge space1.3 Radicals and Rational Exponents
L
latus rectum8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola, 8.3 The Parabola
leading coefficient1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.5 Zeros of Polynomial Functions
leading term1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions
learning sciences1.3 Radicals and Rational Exponents
least common denominator1.6 Rational Expressions, 2.2 Linear Equations in One Variable
least squares regression4.3 Fitting Linear Models to Data
left column1.5 Factoring Polynomials
linchpin topics1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
linear4.3 Fitting Linear Models to Data
linear equation2.2 Linear Equations in One Variable
linear equation with three variables7.2 Systems of Linear Equations: Three Variables
Linear Factorization Theorem5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
linear function4.1 Linear Functions, 4.1 Linear Functions
Linear functions4.1 Linear Functions
linear growth6.1 Exponential Functions
linear model4.2 Modeling with Linear Functions, 4.3 Fitting Linear Models to Data
Linear Regression Model6.8 Fitting Exponential Models to Data
linear relationship4.3 Fitting Linear Models to Data
local extrema3.3 Rates of Change and Behavior of Graphs
local maximum3.3 Rates of Change and Behavior of Graphs, 5.3 Graphs of Polynomial Functions
local minimum3.3 Rates of Change and Behavior of Graphs, 5.3 Graphs of Polynomial Functions
logarithm6.3 Logarithmic Functions
logarithmic equation6.6 Exponential and Logarithmic Equations
Logarithmic Function6.7 Exponential and Logarithmic Models
logarithmic model6.8 Fitting Exponential Models to Data
logistic growth model6.7 Exponential and Logarithmic Models
long division5.4 Dividing Polynomials
lower limit of summation9.4 Series and Their Notations
M
magnitude3.2 Domain and Range, 3.5 Transformation of Functions
main diagonal7.6 Solving Systems with Gaussian Elimination
major and minor axes8.1 The Ellipse
major axis8.1 The Ellipse, 8.1 The Ellipse
matrix7.5 Matrices and Matrix Operations, 7.5 Matrices and Matrix Operations, 7.5 Matrices and Matrix Operations, 7.6 Solving Systems with Gaussian Elimination
matrix multiplication7.5 Matrices and Matrix Operations, 7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
matrix operations7.5 Matrices and Matrix Operations
maximum value5.1 Quadratic Functions
midpoint formula2.1 The Rectangular Coordinate Systems and Graphs
mind map1.5 Factoring Polynomials
minimum value5.1 Quadratic Functions
minor axis8.1 The Ellipse
minor of an entry7.7 Solving Systems with Inverses
model breakdown4.3 Fitting Linear Models to Data
modulus3.2 Domain and Range
monomial1.4 Polynomials, 5.2 Power Functions and Polynomial Functions
Multiplication Principle9.5 Counting Principles, 9.5 Counting Principles
multiplication property2.7 Linear Inequalities and Absolute Value Inequalities
multiplicative inverse7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
multiplicative inverse of a matrix7.7 Solving Systems with Inverses, 7.7 Solving Systems with Inverses
multiplicity5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
mutually exclusive9.5 Counting Principles
mutually exclusive events9.7 Probability
N
n factorial9.1 Sequences and Their Notations
natural exponential function6.1 Exponential Functions
natural logarithm6.3 Logarithmic Functions, 6.6 Exponential and Logarithmic Equations
natural numbers1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials, 3.1 Functions and Function Notation
negative association4.3 Fitting Linear Models to Data
Newton’s Law of Cooling6.7 Exponential and Logarithmic Models
nominal rate6.1 Exponential Functions
nondegenerate conic sections8.4 Rotation of Axes
nonlinear inequality7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
notes during class1.5 Factoring Polynomials
Notice8.2 The Hyperbola
nth partial sum9.4 Series and Their Notations
nth term of the sequence9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations
O
odd function3.5 Transformation of Functions
one-to-one6.2 Graphs of Exponential Functions, 6.3 Logarithmic Functions, 6.5 Logarithmic Properties, 6.5 Logarithmic Properties
one-to-one function3.1 Functions and Function Notation, 3.7 Inverse Functions, 3.7 Inverse Functions
order of magnitude6.7 Exponential and Logarithmic Models
order of operations1.1 Real Numbers: Algebra Essentials
ordered pair2.1 The Rectangular Coordinate Systems and Graphs, 3.1 Functions and Function Notation, 3.2 Domain and Range
ordered triple7.2 Systems of Linear Equations: Three Variables, 7.2 Systems of Linear Equations: Three Variables
origin2.1 The Rectangular Coordinate Systems and Graphs, 3.6 Absolute Value Functions
outcome9.5 Counting Principles
outcomes9.7 Probability
output3.1 Functions and Function Notation
P
parabola5.1 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
parallel2.2 Linear Equations in One Variable
parallel lines4.1 Linear Functions, 4.1 Linear Functions
parent function6.4 Graphs of Logarithmic Functions
partial fraction7.4 Partial Fractions
partial fraction decomposition7.4 Partial Fractions, 7.4 Partial Fractions
Pascal's Triangle9.6 Binomial Theorem
Pascal’s Triangle9.6 Binomial Theorem
perfect square trinomial1.4 Polynomials
periapsis8.5 Conic Sections in Polar Coordinates
perimeter2.3 Models and Applications
permutation9.5 Counting Principles
perpendicular2.2 Linear Equations in One Variable
perpendicular lines4.1 Linear Functions, 4.1 Linear Functions
pH6.5 Logarithmic Properties
piecewise function3.2 Domain and Range
piecewise functions9.1 Sequences and Their Notations
plane7.2 Systems of Linear Equations: Three Variables
point-slope form4.1 Linear Functions
point-slope formula2.2 Linear Equations in One Variable, 8.2 The Hyperbola
polar equation8.5 Conic Sections in Polar Coordinates
polar form of a conic8.5 Conic Sections in Polar Coordinates
polynomial1.4 Polynomials, 1.4 Polynomials, 5.2 Power Functions and Polynomial Functions, 5.5 Zeros of Polynomial Functions
polynomial equation2.6 Other Types of Equations, 5.5 Zeros of Polynomial Functions
polynomial function5.2 Power Functions and Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions
positive association4.3 Fitting Linear Models to Data
power function5.2 Power Functions and Polynomial Functions, 5.2 Power Functions and Polynomial Functions
Power Property6.5 Logarithmic Properties
power rule for logarithms6.5 Logarithmic Properties, 6.5 Logarithmic Properties
principal nth root1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
principal square root1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
probability9.7 Probability
probability model9.7 Probability, 9.7 Probability
probability of an event9.7 Probability
product of two matrices7.5 Matrices and Matrix Operations
Product Property6.5 Logarithmic Properties
product rule for logarithms6.5 Logarithmic Properties, 6.5 Logarithmic Properties
profit function7.1 Systems of Linear Equations: Two Variables
properties of determinants7.8 Solving Systems with Cramer's Rule
Proxima Centauri6.7 Exponential and Logarithmic Models
Pythagorean Theorem2.1 The Rectangular Coordinate Systems and Graphs, 2.5 Quadratic Equations
Q
quadrant2.1 The Rectangular Coordinate Systems and Graphs
quadratic7.4 Partial Fractions, 7.4 Partial Fractions
quadratic equation2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations
quadratic formula2.5 Quadratic Equations, 2.5 Quadratic Equations, 2.5 Quadratic Equations
quadratic function5.1 Quadratic Functions, 5.1 Quadratic Functions, 5.1 Quadratic Functions, 5.1 Quadratic Functions
quotient5.4 Dividing Polynomials
Quotient Property6.5 Logarithmic Properties
quotient rule for logarithms6.5 Logarithmic Properties
R
radical1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
radical equation2.6 Other Types of Equations
radical expression1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents
Radical expressions1.3 Radicals and Rational Exponents
radical functions5.7 Inverses and Radical Functions
radicand1.3 Radicals and Rational Exponents, 1.3 Radicals and Rational Exponents, 2.6 Other Types of Equations
radiocarbon dating6.7 Exponential and Logarithmic Models
radius8.1 The Ellipse
range3.1 Functions and Function Notation, 3.1 Functions and Function Notation, 3.2 Domain and Range, 6.4 Graphs of Logarithmic Functions
rate of change3.3 Rates of Change and Behavior of Graphs, 4.2 Modeling with Linear Functions
rational equation2.2 Linear Equations in One Variable
rational expression1.6 Rational Expressions, 2.2 Linear Equations in One Variable, 7.4 Partial Fractions, 7.4 Partial Fractions, 7.4 Partial Fractions
rational function5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions
rational number2.2 Linear Equations in One Variable
rational numbers1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
Rational Zero Theorem5.5 Zeros of Polynomial Functions, 5.5 Zeros of Polynomial Functions
real number line1.1 Real Numbers: Algebra Essentials
real numbers1.1 Real Numbers: Algebra Essentials
reciprocal2.2 Linear Equations in One Variable, 3.7 Inverse Functions, 5.2 Power Functions and Polynomial Functions
reciprocal function5.6 Rational Functions
recursive formula9.1 Sequences and Their Notations, 9.2 Arithmetic Sequences, 9.2 Arithmetic Sequences, 9.3 Geometric Sequences
Reflect1.5 Factoring Polynomials
reflection6.2 Graphs of Exponential Functions, 6.4 Graphs of Logarithmic Functions
regression analysis6.8 Fitting Exponential Models to Data, 6.8 Fitting Exponential Models to Data, 6.8 Fitting Exponential Models to Data
regression line4.3 Fitting Linear Models to Data
relation3.1 Functions and Function Notation, 3.1 Functions and Function Notation, 3.2 Domain and Range
remainder5.4 Dividing Polynomials
Remainder Theorem5.5 Zeros of Polynomial Functions
removable discontinuity5.6 Rational Functions, 5.6 Rational Functions
Restricting the domain3.7 Inverse Functions
revenue function7.1 Systems of Linear Equations: Two Variables
Richter Scale6.3 Logarithmic Functions
right section1.5 Factoring Polynomials
roots5.1 Quadratic Functions
roster notation9.7 Probability
row7.5 Matrices and Matrix Operations
row matrix7.5 Matrices and Matrix Operations
row operations7.6 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 form7.6 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-equivalent7.6 Solving Systems with Gaussian Elimination
S
sample space9.7 Probability
sample space S9.7 Probability
scalar7.5 Matrices and Matrix Operations
scalar multiple7.5 Matrices and Matrix Operations, 7.5 Matrices and Matrix Operations
scalar multiplication7.5 Matrices and Matrix Operations
scatter plot4.3 Fitting Linear Models to Data, 6.8 Fitting Exponential Models to Data
scatterplot4.3 Fitting Linear Models to Data
scientific notation1.2 Exponents and Scientific Notation, 1.2 Exponents and Scientific Notation, 1.2 Exponents and Scientific Notation
sequence9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.2 Arithmetic Sequences
series9.4 Series and Their Notations, 9.4 Series and Their Notations
set-builder notation2.7 Linear Inequalities and Absolute Value Inequalities, 3.2 Domain and Range
sigma9.4 Series and Their Notations
slope2.2 Linear Equations in One Variable, 3.3 Rates of Change and Behavior of Graphs, 4.1 Linear Functions
slope-intercept4.1 Linear Functions
slope-intercept form4.1 Linear Functions, 4.1 Linear Functions, 4.1 Linear Functions
smooth curve5.2 Power Functions and Polynomial Functions
solution set2.2 Linear Equations in One Variable, 7.2 Systems of Linear Equations: Three Variables
Solutions7.2 Systems of Linear Equations: Three Variables
solving systems of linear equations7.1 Systems of Linear Equations: Two Variables
square matrix7.5 Matrices and Matrix Operations, 7.7 Solving Systems with Inverses, 7.8 Solving Systems with Cramer's Rule
square root property2.5 Quadratic Equations, 8.1 The Ellipse
square trinomial8.1 The Ellipse
standard form2.2 Linear Equations in One Variable
standard form of a quadratic function5.1 Quadratic Functions
standard or graphing form8.1 The Ellipse
stretch6.2 Graphs of Exponential Functions
subsets1.3 Radicals and Rational Exponents
substitution method7.1 Systems of Linear Equations: Two Variables
summarizing the important concepts1.5 Factoring Polynomials
summary1.5 Factoring Polynomials
summation notation9.4 Series and Their Notations, 9.4 Series and Their Notations
surface area5.7 Inverses and Radical Functions
symmetric5.1 Quadratic Functions
synthetic division5.4 Dividing Polynomials, 5.5 Zeros of Polynomial Functions
system of equations7.6 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 equations4.2 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 equations7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of nonlinear inequalities7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
system of three equations in three variables7.8 Solving Systems with Cramer's Rule
T
term5.2 Power Functions and Polynomial Functions, 9.1 Sequences and Their Notations, 9.1 Sequences and Their Notations, 9.2 Arithmetic Sequences
term of a polynomial1.4 Polynomials, 1.4 Polynomials
term of a polynomial function5.2 Power Functions and Polynomial Functions
test questions1.5 Factoring Polynomials
The loudness level, D6.7 Exponential and Logarithmic Models
transformation3.5 Transformation of Functions, 4.1 Linear Functions
transformations3.5 Transformation of Functions
translation8.1 The Ellipse
transverse axis8.2 The Hyperbola, 8.2 The Hyperbola
trinomial1.4 Polynomials, 5.2 Power Functions and Polynomial Functions
turning point5.2 Power Functions and Polynomial Functions, 5.3 Graphs of Polynomial Functions
U
union of two events9.7 Probability
upper limit of summation9.4 Series and Their Notations
upper triangular form7.2 Systems of Linear Equations: Three Variables
V
variable1.1 Real Numbers: Algebra Essentials
varies directly5.8 Modeling Using Variation, 5.8 Modeling Using Variation
varies inversely5.8 Modeling Using Variation
vertex5.1 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 function5.1 Quadratic Functions
vertical asymptote5.6 Rational Functions, 5.6 Rational Functions, 5.6 Rational Functions
vertical compression3.5 Transformation of Functions
vertical line2.2 Linear Equations in One Variable, 4.1 Linear Functions, 4.1 Linear Functions
vertical line test3.1 Functions and Function Notation, 3.7 Inverse Functions
vertical reflection3.5 Transformation of Functions
vertical shift3.5 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 stretch3.5 Transformation of Functions, 4.1 Linear Functions, 6.4 Graphs of Logarithmic Functions
vertices8.1 The Ellipse, 8.1 The Ellipse
volume2.3 Models and Applications
volume of a sphere5.2 Power Functions and Polynomial Functions
W
whole numbers1.1 Real Numbers: Algebra Essentials, 1.1 Real Numbers: Algebra Essentials
X
x-axis2.1 The Rectangular Coordinate Systems and Graphs
x-coordinate2.1 The Rectangular Coordinate Systems and Graphs
x-intercept2.1 The Rectangular Coordinate Systems and Graphs, 4.1 Linear Functions
xx-intercept5.6 Rational Functions
Y
y-axis2.1 The Rectangular Coordinate Systems and Graphs
y-coordinate2.1 The Rectangular Coordinate Systems and Graphs
y-intercept2.1 The Rectangular Coordinate Systems and Graphs, 4.1 Linear Functions
yy-intercept5.6 Rational Functions
Z
Zero Product Property5.3 Graphs of Polynomial Functions
zero-product property2.5 Quadratic Equations
zeros5.1 Quadratic Functions, 5.3 Graphs of Polynomial Functions, 5.3 Graphs of Polynomial Functions, 5.5 Zeros of Polynomial Functions
Zeros of the Function5.5 Zeros of Polynomial Functions
Previous
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/college-algebra-corequisite-support/pages/1-introduction-to-prerequisites
  • 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/college-algebra-corequisite-support/pages/1-introduction-to-prerequisites
Citation information

© Dec 22, 2020 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.