# 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

4.5 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