Graphs of Functions

Graphs of Functions is a Khmer mathematics learning guide for Grade 12 students preparing for Cambodia’s Upper Secondary Education Examination. It develops the concepts and techniques needed to study functions and construct their graphs through explanations, key formulas, worked examples and practice exercises.

The book is organised into three principal sections: rational functions, natural logarithmic functions and exponential functions. It also includes exercises adapted from previous Bac II examinations, French-language mathematics resources and other international learning materials.

This book was compiled as a practical learning and revision resource for Grade 12 students, particularly those preparing for Cambodia’s national Upper Secondary Education Examination.

It introduces the fundamental ideas required to analyse functions and their graphs, including domains, limits, asymptotes, derivatives, extrema, continuity, variation and graphical interpretation. The explanations are supported by worked examples and exercises that allow learners to apply each concept progressively.

The content is divided into three main parts. The first covers rational functions, the second covers natural logarithmic functions and the third covers exponential functions. The later sections include examination-style questions and additional exercises drawn from Cambodian, French and other international mathematics resources.

Readers are encouraged to study each concept carefully, follow the worked solutions and complete the exercises independently to strengthen their mathematical reasoning and examination readiness.

Determine the domain of rational, logarithmic and exponential functions. Calculate limits at the boundaries of a function’s domain. Identify vertical, horizontal and oblique asymptotes. Differentiate functions and use derivatives to study variation. Determine maxima, minima and turning points. Analyse continuity and apply key theorems related to equation roots. Construct variation tables and accurate function graphs. Interpret intersections, symmetry, tangents and graphical solutions. Solve worked problems involving rational functions. Apply the properties of natural logarithmic functions. Apply the properties of exponential functions. Practise previous Bac II questions and additional examination-style exercises.

I would like to express my sincere gratitude to the teachers, students, readers and supporters who encouraged the preparation and publication of this mathematics book.

I am grateful to the review committee and fellow mathematics learners who contributed feedback and helped improve the material. I also appreciate everyone who supported and purchased my mathematics publications, as their encouragement played an important role in bringing this work to completion.

I acknowledge the authors, educators and institutions whose mathematics resources are referenced in the book. Their work supported the research, comparison and development of the exercises included in this publication.