Unit 1 – Functions Characteristics and Properties
Functions in mathematics possess various characteristics and properties that describe their behavior and relationships with their inputs and outputs. Here are some common characteristics and properties of functions:
Domain, Range, Function Notation, Even and Odd Functions, Periodic Functions, Exploring Absolute Value, Properties of Graphs of Functions, Inverse Relations, Piecewise Functions
These are just a few of the characteristics and properties that describe functions. The study of functions involves analyzing their behavior, graphing them, understanding their relationships, and applying various mathematical tools to solve problems and make predictions.
Unit 2 – Polynomial Functions
Polynomial functions are mathematical functions that consist of a sum of terms, each of which is a constant multiplied by a variable raised to a non-negative integer exponent.
Key characteristics and properties of polynomial functions include Degree, Leading Coefficient, Constant Term, Roots and Zeros, Fundamental Theorem of Algebra, Polynomial Division, Polynomial Factoring, Polynomial Long Division:
Polynomial functions are widely used in various fields, including mathematics, physics, engineering, economics, and computer science. They provide a flexible framework for modeling and analyzing relationships between variables, solving equations, and making predictions. Understanding polynomial functions and their properties is crucial for many areas of mathematical study and practical applications.
Unit 3 – Polynomial Equations and Inequalities
Polynomial equations and inequalities involve expressions with polynomial functions and the equalities or inequalities between them. Solving polynomial equations and inequalities is an important part of algebra and calculus, and it involves finding the values of the variable that satisfy the given conditions.
Key concepts related to polynomial equations and inequalities are Polynomial Equations, Zeroes or Roots, Degree and Number of Roots, Factoring, Quadratic Formula, Polynomial Inequalities, Polynomial inequality, Interval Notation, Sign Analysis.
Solving polynomial equations and inequalities often involves techniques such as factoring, using formulas for quadratic and cubic equations, employing synthetic or long division, and applying algebraic manipulation. These concepts are crucial in various fields, including mathematics, physics, engineering, and economics, where polynomial equations and inequalities are used to model and solve real-world problems.
