Lesson Plan

• Define a function and correctly identify its domain and range.
• Distinguish one‑one and many‑one functions using the horizontal line test.
• Find the inverse of a one‑one function algebraically.
• Compose two functions and determine the domain of the composition.
• Apply these concepts to solve short contextual problems.

• Projector or interactive whiteboard
• Teacher‑prepared slides/handout with definitions, tables and examples
• Worksheet with practice problems on domain, range, inverse and composition
• Graph paper and calculators
• Set of function cards for quick‑fire matching activity

Begin with a quick real‑world example (e.g., a vending machine) to illustrate the idea of a rule that gives a single output for each input. Review the previous lesson on basic algebraic expressions and ask students to state what they already know about inputs and outputs. Explain that today’s success criteria are to identify domains/ranges, test functions for one‑to‑one behaviour, and construct inverses and compositions.

1. Do‑now (5'): Students complete a short quiz on identifying domain and range from given formulas.
2. Direct instruction (10'): Present definitions of function, domain, range, and illustrate one‑one vs many‑one with graphs.
3. Guided practice (15'): Work through horizontal line test examples together, checking understanding with quick polls.
4. Collaborative activity (10'): In pairs, use function cards to match functions with their correct classification and justify using the test.
5. Inverse function demonstration (10'): Show algebraic steps to find an inverse, then have students verify with a partner.
6. Composition practice (10'): Model composition of two functions, then students solve a worksheet problem applying domain restrictions.
7. Exit ticket (5'): Write one example of a function, state its domain, and indicate whether it has an inverse.

Summarise the key ideas: a function’s domain and range, the horizontal line test for one‑to‑one, how to obtain an inverse, and the steps for composing functions. Collect the exit tickets to gauge immediate understanding and assign a worksheet for homework that reinforces finding domains, inverses, and compositions.