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College Algebra with Corequisite Support

Key Terms

College Algebra with Corequisite SupportKey Terms
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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

Key Terms

absolute maximum
the greatest value of a function over an interval
absolute minimum
the lowest value of a function over an interval
average rate of change
the difference in the output values of a function found for two values of the input divided by the difference between the inputs
composite function
the new function formed by function composition, when the output of one function is used as the input of another
decreasing function
a function is decreasing in some open interval if f( b )<f( a ) f( b )<f( a ) for any two input values a a and b b in the given interval where b>a b>a
dependent variable
an output variable
domain
the set of all possible input values for a relation
even function
a function whose graph is unchanged by horizontal reflection, f(x)=f(−x), f(x)=f(−x), and is symmetric about the y- y- axis
function
a relation in which each input value yields a unique output value
horizontal compression
a transformation that compresses a function’s graph horizontally, by multiplying the input by a constant b>1 b>1
horizontal line test
a method of testing whether a function is one-to-one by determining whether any horizontal line intersects the graph more than once
horizontal reflection
a transformation that reflects a function’s graph across the y-axis by multiplying the input by −1 −1
horizontal shift
a transformation that shifts a function’s graph left or right by adding a positive or negative constant to the input
horizontal stretch
a transformation that stretches a function’s graph horizontally by multiplying the input by a constant 0<b<1 0<b<1
increasing function
a function is increasing in some open interval if f( b )>f( a ) f( b )>f( a ) for any two input values a a and b b in the given interval where b>a b>a
independent variable
an input variable
input
each object or value in a domain that relates to another object or value by a relationship known as a function
interval notation
a method of describing a set that includes all numbers between a lower limit and an upper limit; the lower and upper values are listed between brackets or parentheses, a square bracket indicating inclusion in the set, and a parenthesis indicating exclusion
inverse function
for any one-to-one function f(x), f(x), the inverse is a function f −1 (x) f −1 (x) such that f −1 ( f( x ) )=x f −1 ( f( x ) )=x for all x x in the domain of f; f; this also implies that f( f −1 ( x ) )=x f( f −1 ( x ) )=x for all x x in the domain of f −1 f −1
local extrema
collectively, all of a function's local maxima and minima
local maximum
a value of the input where a function changes from increasing to decreasing as the input value increases.
local minimum
a value of the input where a function changes from decreasing to increasing as the input value increases.
odd function
a function whose graph is unchanged by combined horizontal and vertical reflection, f(x)=−f(−x), f(x)=−f(−x), and is symmetric about the origin
one-to-one function
a function for which each value of the output is associated with a unique input value
output
each object or value in the range that is produced when an input value is entered into a function
piecewise function
a function in which more than one formula is used to define the output
range
the set of output values that result from the input values in a relation
rate of change
the change of an output quantity relative to the change of the input quantity
relation
a set of ordered pairs
set-builder notation
a method of describing a set by a rule that all of its members obey; it takes the form {x|statement about x} {x|statement about x}
vertical compression
a function transformation that compresses the function’s graph vertically by multiplying the output by a constant 0<a<1 0<a<1
vertical line test
a method of testing whether a graph represents a function by determining whether a vertical line intersects the graph no more than once
vertical reflection
a transformation that reflects a function’s graph across the x-axis by multiplying the output by −1 −1
vertical shift
a transformation that shifts a function’s graph up or down by adding a positive or negative constant to the output
vertical stretch
a transformation that stretches a function’s graph vertically by multiplying the output by a constant a>1 a>1
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