Functions
Part 4: Hyperbola
Gr 10

The Grade 10 Hyperbola module introduces learners to rational functions and helps them understand how hyperbolic graphs behave and how their key features are identified. This chapter expands students’ understanding of functions beyond straight lines and parabolas, preparing them for the full range of graphs encountered in higher grades.

Learners explore the standard form of the hyperbola, y=ax+qy = \frac{a}{x} + qy=xa​+q, and investigate how the values of aaa and qqq influence the graph’s shape, position, and orientation. Lessons cover identifying asymptotes, determining intercepts, understanding the effect of reflections, and sketching hyperbolas accurately using key points. Students also learn how to interpret real-life scenarios represented by hyperbolic relationships and how to compare different hyperbolic graphs.

By the end of this module, learners will be able to recognise, sketch, and analyse hyperbolas, understand the role of asymptotes, and apply hyperbolic functions effectively in algebraic and graphical problem-solving—building the foundation for advanced function work in Grades 11 and 12.