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Kansas State University Polytechnic Campus
2310 Centennial Rd.
Salina, KS 67401

College Algebra
© Teresa Hartman

Chapter R - Review of Prerequisites

R.1 Fractions, and Rules of Order
Fractions / Introduction to Exponents and Roots / Rules of Order

R.2 The Number Line
Number Line / Operations on Positive and Negative Numbers / Interval and Set-Builder Notation / Absolute Value

R.3 The Real Number System
Classification of Real Numbers / Properties of Real Numbers / Evaluating a Variable Expression

R.4 Exponents
Integer Exponents / Scientific Notation

R.5 Polynomials
Identifying Polynomials / Polynomial Vocabulary and Classification / Adding, Subtracting, and Multiplying Polynomials

R.6 Factoring
Common Factor / Factor by Grouping / Trinomial / Difference of Squares / Sum and Difference of Cubes / Factoring Completely

R.7 Rational Expressions
Simplifying, Multiplying, and Dividing Rational Expressions / Adding and Subtracting Rational Expressions / Complex Rational Expressions / Restricted Values

R.8 Radical Notation and Rational Exponents
Simplifying Radical Expressions / Adding, Subtracting, and Multiplying Radical Expressions / Rationalizing the Denominator / Rational Exponents

 

Chapter 1 - Solving Equations

1.1 Solving Linear and Rational Equations
Solving Linear Equations / Solving Rational Equations

1.2 Solving Linear Inequalities
Solving an Equation for a Specified Variable (no numbers) / Solving Linear Inequalities / Solving Compound Inequalities

1.3 Complex Numbers
All Operations Over Complex Numbers

1.4 Solving Quadratic Equations by Factoring and Square Root Method
Factoring/Square Root Method

1.5 Solving Quadratic Equations by the Quadratic Formula
Quadratic Formula / Best Methods Practices

1.6 Solving Quadratic Equations by Completing the Square and Look-a-likes
Completing the Square / Look-a-Likes

1.7 Solving Other Equations
Higher Polynomials / Radical Equations / Etc. 

 

Chapter 2 - Graphing and Functions

2.1 Introduction to Graphing
Distance / Midpoint / Circles

2.2 Graphing by Plotting points
Plotting points / x- and y-intercepts / Function Notation / Graphing Calculator Checks

2.3 Graphing Linear Functions
Slope / Graphing using slope and y-intercept / Writing Equations of Lines / Horizontal and Vertical Lines / Graphing Calculator Checks

2.4 Quadratic Functions
Vertex Form Equation / Analyzing Quadratic Graphs / Vertex Formula 

2.5 Piecewise Functions and Analyzing Graphs
Evaluating Piecewise Functions / Graphing Piecewise Functions with and without the Graphing Calculator / Analyzing graphs to determine Increasing, Decreasing, Constant, Maximum, and Minimum

2.6 Function Relations, Domain and Range
Identifying a Function given Sets and Graphs / Finding Domain and Range given Functions and Graphs / Interpreting all parts of a Function 

2.7 Algebra, Composition, and Symmetry of Functions
Combining Functions / Composing and Decomposing Functions / Difference Quotient / Symmetry towards x-axis, y-axis, and origin / Even and Odd Functions

2.8 Transformations of Graphs
Basic Graphs and their Intercepts, Domain, Range / Shifts / Reflections / Stretching and Shrinking 

 

Chapter 3 - Polynomial and Rational Functions

3.1 Graphing Polynomial Functions
End Behavior / y-intercept / x-intercepts, zeros, and multiplicities / graphing polynomial functions / (Coming soon: Checking all steps with the graphing calculator!)

3.2 Polynomial Division
Polynomial Long Division / Polynomial Synthetic Division / Remainder Theorem / Factor Theorem / Using Polynomial Division to Factor Polynomials

3.3 Zeros of Polynomials
Rational Zeros Theorem / Conjugate Zeros Theorem / Finding Zeros of any Format / Building a Polynomial Given Zeros

3.4 Graphing Rational Functions
Finding Vertical Asymptotes / Finding Horizontal and Oblique Asymptotes / Causes of Holes in Graph / Sketching Graphs of Rational Functions 

3.5 Solving Polynomial and Rational Inequalities 
Solving Polynomial Inequalities / Solving Rational Inequalities / Special Cases / Applied Examples

 

Chapter 4 - Exponential and Logarithmic Functions

4.1 Inverse Functions
Definition / One-to-One Functions / How to find an Inverse Function / Composition / Graphing Inverse Functions

4.2 Exponential Functions
Graphs and Characteristics of Exponential Functions / Graphing using Transformations / Comound Interest / The Natural Function, e / Compounding Continuously / 

4.3 Logarithmic Functions
Definition / Common and Natural Logs / Graphs and Characteristics of Logarithmic Functions / Graphing using Transformations

4.4 Properties of Logarithms

4.5 Exponential and Logarithm Equations

 

Chapter 5 - Systems of Equations

5.1 Solving Systems of Equations by Substitution or Elimination Method

5.2 Matrix Methods
Solving systems of equations by the Guass-Jordan Method