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A deep understanding of relations and functions is the cornerstone of calculus and coordinate geometry. This text-based course is designed to take you from fundamental definitions to the analytical thinking required for high-stakes engineering entrance exams. You will learn how to break down complex mathematical mappings, analyze domain and range constraints, and interpret function behavior systematically. What you will learn: Understand the core principles of Cartesian products, relations, and equivalence classes; Master different types of functions including injective, surjective, and bijective mappings; Analyze and sketch graphs of polynomial, rational, trigonometric, and logarithmic functions; Apply graph transformations to solve complex equations and inequalities; Solve step-by-step practice problems modeled on past exam patterns. This course begins with essential terminology and foundational set theory before moving into advanced function types, graphical analysis, and rigorous algebraic proofs. It is designed for students preparing for competitive engineering exams who want to build a rock-solid mathematical foundation from scratch. Start reading today to sharpen your mathematical reasoning and master algebraic functions.