- 1 Functions and Graphs Contents
- 1.1 Function Families
- 1.2 Graphical Transformations
- 1.3 Point Notation and Function Notation
- 1.4 Domain and Range
- 1.5 Maximums and Minimums
- 1.6 Symmetry
- 1.7 Increasing and Decreasing
- 1.8 Zeroes and Intercepts of Functions
- 1.9 Asymptotes and End Behavior
- 1.10 Continuity and Discontinuity
- 1.11 Function Composition
- 1.12 Inverses of Functions
- 1.13 References
- 2 Polynomials and Rational Functions
- 2.1 Factoring Review
- 2.2 Advanced Factoring
- 2.3 Polynomial Expansion and Pascal’s Triangle
- 2.4 Rational Expressions
- 2.5 Polynomial Long Division and Synthetic Division
- 2.6 Solving Rational Equations
- 2.7 Holes in Rational Functions
- 2.8 Zeroes of Rational Functions
- 2.9 Vertical Asymptotes
- 2.10 Horizontal Asymptotes
- 2.11 Oblique Asymptotes
- 2.12 Sign Test for Rational Function Graphs
- 2.13 Graphs of Rational Functions by Hand
- 2.14 References
- 3 Logs and Exponents
- 3.1 Exponential Functions
- 3.2 Properties of Exponents
- 3.3 Scientific Notation
- 3.4 Properties of Logs
- 3.5 Change of Base
- 3.6 Exponential Equations
- 3.7 Logistic Functions
- 3.8 References
- 4 Basic Triangle Trigonometry
- 4.1 Angles in Radians and Degrees http://www.ck12.org Contents
- 4.2 Circular Motion and Dimensional Analysis
- 4.3 Special Right Triangles
- 4.4 Right Triangle Trigonometry
- 4.5 Law of Cosines
- 4.6 Law of Sines
- 4.7 Area of a Triangle
- 4.8 Applications of Basic Triangle Trigonometry
- 4.9 References
- 5 Trigonometric Functions
- 5.1 The Unit Circle
- 5.2 The Sinusoidal Function Family
- 5.3 Amplitude of Sinusoidal Functions
- 5.4 Vertical Shift of Sinusoidal Functions
- 5.5 Frequency and Period of Sinusoidal Functions
- 5.6 Phase Shift of Sinusoidal Functions
- 5.7 Graphs of Other Trigonometric Functions
- 5.8 Graphs of Inverse Trigonometric Functions
- 5.9 References
- 6 Analytic Trigonometry
- 6.1 Basic Trigonometric Identities
- 6.2 Pythagorean Identities
- 6.3 Sum and Difference Identities
- 6.4 Double, Half, and Power Reducing Identities
- 6.5 Trigonometric Equations
- 6.6 References
- 7 Vectors
- 7.1 Basic Properties of Vectors
- 7.2 Operations with Vectors
- 7.3 Resolution of Vectors into Components
- 7.4 Dot Product and Angle Between Two Vectors
- 7.5 Vector Projection
- 7.6 References
- 8 Systems and Matrices
- 8.1 Systems of Two Equations and Two Unknowns
- 8.2 Systems of Three Equations and Three Unknowns
- 8.3 Matrices to Represent Data
- 8.4 Matrix Algebra
- 8.5 Row Operations and Row Echelon Forms
- 8.6 Augmented Matrices
- 8.7 Determinant of Matrices
- 8.8 Cramer’s Rule
- 8.9 Inverse Matrices
- 8.10 Partial Fractions
- 8.11 References
- 9 Conics
- 9.1 General Form of a Conic
- 9.2 Parabolas Contents http://www.ck12.org
- 9.3 Circles
- 9.4 Ellipses
- 9.5 Hyperbolas
- 9.6 Degenerate Conics
- 9.7 References
- 10 Polar and Parametric Equations
- 10.1 Polar and Rectangular Coordinates
- 10.2 Polar Equations of Conics
- 10.3 Parameters and Parameter Elimination
- 10.4 Parametric Inverses
- 10.5 Applications of Parametric Equations
- 10.6 References
- 11 Complex Numbers
- 11.1 Fundamental Theorem of Algebra
- 11.2 Arithmetic with Complex Numbers
- 11.3 Trigonometric Polar Form of Complex Numbers
- 11.4 De Moivre’s Theorem and nth Roots
- 11.5 References
- 12 Discrete Math
- 12.1 Recursion
- 12.2 Arithmetic and Geometric Sequences
- 12.3 Sigma Notation
- 12.4 Arithmetic Series
- 12.5 Geometric Series
- 12.6 Counting with Permutations and Combinations
- 12.7 Basic Probability
- 12.8 Binomial Theorem
- 12.9 Induction Proofs
- 12.10 References
- 13 Finance
- 13.1 Simple Interest
- 13.2 Compound Interest per Year
- 13.3 Compound Interest per Period
- 13.4 Continuous Interest
- 13.5 APR and APY (Nominal and Effective Rates)
- 13.6 Annuities
- 13.7 Annuities for Loans
- 14 Concepts of Calculus
- 14.1 Limit Notation
- 14.2 Graphs to Find Limits
- 14.3 Tables to Find Limits
- 14.4 Substitution to Find Limits
- 14.5 Rationalization to Find Limits
- 14.6 One Sided Limits and Continuity
- 14.7 Intermediate and Extreme Value Theorems
- 14.8 Instantaneous Rate of Change
- 14.9 Area Under a Curve http://www.ck12.org Contents
- 14.10 References
- 15 Concepts of Statistics
- 15.1 Mean, Median and Mode
- 15.2 Expected Value and Payoffs
- 15.3 Five Number Summary
- 15.4 Graphic Displays of Data
- 15.5 Variance
- 15.6 The Normal Curve
- 15.7 Linear Correlation
- 15.8 Modeling with Regression
- 15.9 References
- 16 Logic and Set Theory
- 16.1 And and Or Statements
- 16.2 If-Then Statements
- 16.3 Negative Statements
- 16.4 Inverse, Converse, and Contrapositive
- 16.5 References
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