Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Mathematics
Lesson Topic: Functions: notation, domain and range, composite and inverse functions, sketching graphs
Learning Objective/s:
  • Describe function notation and clearly state domain and range.
  • Determine the domain and range of algebraic functions using restriction rules.
  • Construct composite functions and identify their domains.
  • Find inverse functions algebraically and verify one‑to‑one status.
  • Sketch accurate graphs by applying a systematic checklist (intercepts, asymptotes, critical points, concavity).
Materials Needed:
  • Projector or interactive whiteboard
  • Printed worksheet with practice problems
  • Graph paper and rulers
  • Scientific calculators
  • Set of function cards for quick matching
  • Whiteboard markers
 Introduction:
Begin with a quick poll: “What does the notation f(x) represent?” Review prior work on linear functions and their graphs. Explain that today’s success criteria are to correctly identify domain/range, compose and invert functions, and produce accurate sketches.
Lesson Structure:
  1. Do‑Now (5’) – Short quiz on function notation and domain identification.
  2. Mini‑lecture (15’) – Review domain/range rules, composite function definition, and inverse process with screen examples.
  3. Guided practice (20’) – Pairs work on composite and inverse examples while teacher checks understanding.
  4. Graphing checklist demonstration (10’) – Demonstrate systematic graphing steps on a sample function.
  5. Independent activity (15’) – Students sketch graphs of two assigned functions, annotating domain, intercepts, asymptotes, and turning points.
  6. Exit ticket (5’) – Write one key step for finding an inverse and one tip for sketching a graph.
Conclusion:
Summarise how domain analysis, composition, and inversion underpin accurate graphing. Collect exit tickets that recap the graphing checklist. Assign homework: complete the remaining sketching problems on the worksheet and be ready to present solutions tomorrow.