Concept Overview

Functions and Graphs

• Definition of a function

• Domain and range

• Types of functions: Linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric, piecewise

• Graphing techniques (translations, reflections, stretching/compressing)

• Inverse functions

• Composition of functions

Polynomial and Rational Functions

• Factoring polynomials

• Zeros of polynomial functions

• Polynomial division (long division, synthetic division)

• Rational functions and asymptotes (vertical, horizontal, and oblique)

• Graphing rational functions

Exponential and Logarithmic Functions

• Exponential functions and their properties

• Logarithmic functions and their properties

• Solving exponential and logarithmic equations

• Laws of logarithms

• Applications of exponential and logarithmic functions

Trigonometry

• Unit circle

• Radian and degree measure

• Trigonometric functions: sine, cosine, tangent, secant, cosecant, cotangent

• Graphing trigonometric functions

• Inverse trigonometric functions

• Trigonometric identities: Pythagorean, reciprocal, quotient, and co-function identities

• Solving trigonometric equations

• Law of Sines and Law of Cosines

• Applications of trigonometry

Sequences and Series

• Arithmetic sequences and series

• Geometric sequences and series

• Binomial theorem

• Convergence and divergence of series

Matrices and Determinants

• Matrix operations (addition, subtraction, multiplication)

• Determinants and properties

• Inverse of a matrix

• Solving systems of equations using matrices

Vectors and Parametric Equations

• Introduction to vectors (magnitude and direction)

• Vector operations (addition, scalar multiplication, dot product)

• Parametric equations and graphs

Conic Sections

• Parabolas

• Circles

• Ellipses

• Hyperbolas

• Equations and graphs of conic sections

• Applications of conic sections

Limits and Continuity (Introduction to Calculus)

• Understanding limits

• Limit properties

• Continuity of functions

• One-sided limits

• Basic concepts of derivatives and integrals (brief introduction)

Complex Numbers

• Imaginary and complex numbers

• Operations with complex numbers (addition, subtraction, multiplication, division)

• Polar form of complex numbers

• De Moivre’s Theorem