Foundational Math: Functions and Algebraic Inequalities

Functions and inequalities are the essential language of advanced mathematics, forming the basis for calculus and complex problem-solving. Without a solid understanding of these core concepts, tackling higher-level studies becomes impossible. This course provides a rigorous, text-based introduction to foundational mathematical analysis. You will master the systematic methods required to define, manipulate, and solve complex functions and algebraic inequalities, preparing you for success in advanced mathematical fields. What you'll learn: * Understand the definitions and classifications of relations, functions, and inverse functions. * Master systematic methods for finding the domain and range of complex algebraic functions. * Solve linear, polynomial, rational, and absolute value inequalities using critical point analysis. * Analyze the behavior of functions using concepts like monotonicity and symmetry. * Apply algebraic methods to solve systems of inequalities and piecewise-defined functions. This text-only course begins with core terminology and definitions, moving methodically through algebraic techniques for manipulating expressions, and concluding with focused practice exercises on function analysis and inequality solving. The material emphasizes reading and understanding the underlying mathematical principles. This course is designed for absolute beginners in advanced mathematics, high school students, or anyone needing to strengthen their foundational knowledge. No prior experience beyond basic algebra is required. Develop the analytical skills necessary for success in advanced mathematical fields.