Year 11 - Maths
Checking and securing understanding of functions
Functions and proof
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will further develop their understanding of algebraic notation and graphs by learning about functions, their inverses and composite functions.
Lesson Summary
You will learn to appreciate that a function is a mathematical relationship that uniquely maps a set of numbers onto another set of numbers.
Key Notes
- A function has a set of inputs and outputs.
- For any valid input, there is an output.
- A function takes an input and performs a series of operations, leading to an output.
- The set of inputs is called the domain.
- The set of outputs is called the range.
Vocabulary To Learn
- Function: A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
- Domain: The domain of a function is the set of values that the mapping is performed on.
- Range: The range of a function is the set of values mapped to by the function and the stated domain.
Common Mistakes To Avoid
- Pupils may confuse the domain and the range.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A function has a set of inputs and outputs. For any valid input, there is an output.
2. Use this key word in a maths sentence and explain it clearly. 'Function'
A function is a mathematical relationship that uniquely maps values of one set to the values of another set. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may confuse the domain and the range. Correction: Drawing the graph of the function and labelling the axes correctly will help pupils connect domain and range.
More Lessons In This Unit
- Defining function notation Study Guide
- Finding the inverse of a function Study Guide
- General algebraic forms for specific number properties Study Guide
- Logical arguments Study Guide
- Making conjectures about patterns and relationships Study Guide
- Multiple approaches to logical arguments Study Guide
- Problem solving with functions and proof Study Guide
- Proving or disproving a statement Study Guide
- Solving equations involving composite functions Study Guide
- Solving equations involving functions Study Guide
- Writing a generalised statement about specific number properties Study Guide
- Writing a proof Study Guide
- Writing composite functions Study Guide
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