Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Find the domain and range of functions, including inverse and composite functions
Learning Objective/s:
  • Describe the concepts of domain and range and identify restrictions that make an expression undefined.
  • Determine the domain and range of rational, radical, logarithmic and composite functions using algebraic and graphical methods.
  • Construct composite functions, find their domains, and simplify the resulting expressions.
  • Find the inverse of a one‑to‑one function algebraically and state its domain and range.
  • Apply these techniques to solve exam‑style problems accurately.
Materials Needed:
  • Projector and screen for slides/graph sketches
  • Whiteboard and markers
  • Student worksheets with worked examples and practice questions
  • Graphing calculators or a computer algebra system (e.g., Desmos)
  • Handout summarising domain/range rules and steps for finding inverses
 Introduction:
Begin with a quick poll: which functions have you found tricky to determine domain or range? Recall that a function assigns each input a single output, and that domain and range are the sets of permissible inputs and possible outputs. Today we will master systematic methods for finding domains, ranges, composites and inverses, and you will demonstrate these in a short exit ticket.
Lesson Structure:
  1. Do‑now (5') – Students complete a short worksheet identifying domain restrictions for several expressions.
  2. Mini‑lecture (10') – Review definitions, domain/range rules, and composite/inverse concepts with projected examples.
  3. Guided practice (15') – Work through Example 1 (rational function) and Example 2 (composite) as a class, prompting students to articulate each step.
  4. Independent practice (15') – Pairs solve the three practice questions on domain, composite, and inverse functions while the teacher circulates.
  5. Quick check (5') – Exit ticket: write one method for finding a function’s range and one condition for a function to have an inverse.
  6. Homework (brief) – Assign additional domain, range, composite and inverse problems from the textbook.
Conclusion:
Summarise that domain is found by preventing undefined expressions, while range follows from solving for y or using known function ranges. Remind students that composite domains combine the restrictions of each component and that inverses exist only for one‑to‑one functions. Collect exit tickets and assign homework to reinforce today’s techniques.