Functions
Gr12

The Grade 12 Functions module brings together and extends all the foundational function concepts learned in previous grades. This chapter focuses on advanced function analysis, transformations, inverses, and the interpretation of complex graphs—skills that are essential for success in Grade 12 examinations and university-level mathematics.

Learners explore a variety of function types, including linear, quadratic, hyperbolic, exponential, and logarithmic functions. The lessons cover domain and range, asymptotes, intercepts, turning points, and key features of each function. Students also learn how to apply transformations such as shifts, reflections, stretches, and compressions, and how these affect the graph and equation of a function. A significant component of the module involves working with inverse functions, understanding the conditions under which an inverse exists, and interpreting the inverse graphically and algebraically.

By the end of this module, learners will be able to analyse, sketch, and compare different functions with confidence, apply transformations systematically, and interpret inverse and composite functions accurately. These skills form a crucial foundation for calculus, advanced graph analysis, and a wide range of mathematical applications beyond school.