Algebra Notes and Example Problems
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Key topics in each document are noted with bulletpoints.
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- Basics of Graphing
- Graphing by Plotting Points
- x-and y-intercepts
- Slope of a Line
- Equation of a Line (Linear Equations)
- Horizontal Lines, Vertical Lines
- Graphing using Slope and y-intercept
- Formulas
- Writing Equations
- Parallel and Perpendicular Lines
- Negative Exponents
- Rational (Fractional) Exponents
- Types of Solutions
- Solve by Graphing
- Substitution Method
- Elimination Method
- Systems of Equations with Three Variables
- Steps to Factoring Polynomials
- Greates Common Factor (GCF)
- Factor by Grouping
- Factoring Trinomials
- AC Method
- Difference of Squares
- Difference of Cubes
- Solve Quadratic Equations by Factoring
- Simplifying Rational Expressions
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Complex Rational Expressions (Complex Fractions)
- Solve Rational Equations
- Functions
- Vertical Line Test
- Evaluating Functions
- Difference Quotient
- Domain and Range
- One-to-One Functions
- Horizontal Line Test
Parent Functions (Library of Functions)
- Graphs of Parent Functions
- Graphs of Other Common Equations
- Common Polar Graphs
- Piecewise Functions
- Graphing Piecewise Functions
- Vertical, Horizontal Shift
- Stretch Vertically, Horizontally
- Reflection over the x-axis, y-axis
- Compress Vertically, Horizontally
- Parabola
- Vertex
- Maximum and Minimum
- Solve Quadratic Equations by Factoring
- Solve Quadratic Equations by Square Root Method
- Quadratic Formula
- End Behavior
- Zeros of Polynomial Functions
- Multiplicity
- Rational Zero Theorem
- Factor Theorem
- Descartes Rule of Signs
- Remainder Theorem
- Composite Function Notation
- Decomposition of Functions
- Domain of Composite Functions
- Properties of Inverse Functions
- Verify Inverse Functions
- Graphs of Inverse Functions
- Vertical Asymptotes
- Horizontal Asymptotes
- Oblique (Slant) Asymptotes
- Graphing Rational Functions
Exponential and Logarithmic Functions
- Properties of Exponential Functions
- Log Rules and Properties
- Expanding and Condensing Logarithms
- Converting between Log and Exponential Form
- Solving Exponential and Log Equations