Foundations of Algebra: Functions and Inequalities

Strong algebraic skills are the bedrock of calculus, coordinate geometry, and advanced technical fields, yet many learners struggle with the core behavior of functions and inequalities. This text-based course guides you through foundational mathematical relationships, helping you decode complex functional behavior and solve multi-step inequalities with confidence. Through clear, written explanations and structured examples, you will learn to analyze and manipulate the essential mathematical tools used in higher education and technical disciplines. What you'll learn: - Understand the core properties and behaviors of polynomial, logarithmic, and modulus functions - Analyze advanced mathematical relations like the greatest integer and fractional part functions - Solve complex algebraic inequalities using systematic sign-chart and interval methods - Identify domain and range restrictions to solve mathematical constraints accurately - Apply fundamental algebraic properties to simplify and solve composite functions - Practice step-by-step problem-solving techniques through written exercises and detailed breakdowns Starting with basic definitions of relations, mappings, and interval notation, you will progress systematically through specific function families and their corresponding inequality rules. This course is designed for beginners, pre-calculus students, and anyone preparing for advanced mathematics exams who wants to build a flawless mathematical foundation from the ground up. Start reading today to unlock your mathematical potential.