Foundational Mathematics: Functions, Graphs, and Inequalities

Many students struggle with higher mathematics because their fundamental understanding of functions and algebraic manipulation is weak. This course provides a robust foundation in essential pre-calculus topics, enabling you to confidently analyze mathematical relationships, solve complex inequalities, and interpret functions graphically. What you'll learn: * Understand the precise definitions of functions, relations, domain, and range using standard mathematical notation. * Master rigorous techniques for solving linear, quadratic, rational, and absolute value inequalities. * Practice sketching and interpreting the graphs of core functions, including common transformations and shifts. * Apply algebraic methods to determine the domain and range of complex functional expressions and composite functions. * Learn the foundational concepts of piecewise functions and basic compositional analysis. The course begins with defining basic mathematical objects and notation, gradually progressing into detailed analysis of functions, their properties, and rigorous methods for solving inequalities. You will apply these concepts through extensive practice focused on algebraic manipulation and graphical interpretation. This course is designed for absolute beginners or those needing a thorough review of pre-calculus fundamentals before moving on to higher-level math or STEM fields. No prior advanced mathematical knowledge is required. Start building your strong mathematical foundation today.