About this unit
How does writing a relationship as a function help us describe and predict change?
Sections in this unit
Factual
- What does f(3) ask you to do?
- What are the domain and the range of a function?
- How do you read a value off the graph of a function?
Conceptual
- What changes when the input to a function is an expression rather than a number?
- Why are a straight line, a regression equation and a function machine the same idea in three notations?
Debatable
- Is a function a rule, a machine, or a set of pairs?
Skills
Students should be able to:
- Use correct notation, and read what a piece of notation asserts before acting on it.
- Move between representations: read the same function as notation, as a graph and as a rule in words.
- Interpret a mathematical result in the context it came from, with its units stated.
- Select and apply an appropriate technique in an unfamiliar situation.
How you are assessed
- End-of-year cumulative paper, Criterion A
Before you start
Students arrive with:
- Function machines and mapping diagrams from Year 9, where input and output are already familiar.
- Substitution into an expression, from Unit 3.
- The equation of a straight line, gradient and intercept, from Unit 4.
- The regression equation as a rule relating two quantities, from Unit 6 — a function in all but notation.
- Optimisation and the maximum of a quadratic, from Unit 3, which this unit revisits in function language.
Check what you remember
The equation of a straight line