1. Functions
- Syllabus
- 0606–2028–2029
- Topic
- 1
- Level
- —
1.1. Understand function terminology
- Understand the terms: function, domain, range (image set), one-one function, many-one function, inverse function and composition of functions.
- Includes explaining in words why a given relation is a function.
1.2. Find domains and ranges of functions
- Find the domain and range of functions, including inverse and composite functions.
- Restrict the domain of f where needed for f^-1 and/or gf to exist.
- Understand that the domain of gf is a subset of the domain of f, and the range of gf is a subset of the range of g.
1.3. Use function notation
- Recognise and use function notation such as f(x), f: x -> lg x, f^-1(x), fg(x) = f(g(x)) and f^2(x) = f(f(x)).
- The notation f^2(x) will not be used with trigonometric functions.
1.4. Relate y = f(x) and y = |f(x)|
- Understand the relationship between y = f(x) and y = |f(x)| where f(x) may be linear, quadratic, cubic or trigonometric.
- For trigonometric functions, use y = a sin bx + c, y = a cos bx + c or y = a tan bx + c, where a is a positive integer, b is a simple fraction or integer, and c is an integer.
- Fractions for b have denominator 2, 3, 4, 6 or 8 only.
1.5. Explain when inverses do not exist
- Explain in words why a given function does not have an inverse.
1.6. Find inverse functions
- Find the inverse of a one-one function.
- Use correct inverse-function notation.
1.7. Form and use composite functions
- Form and use composite functions.
- Understand that the order of functions is important, so fg may not be the same as gf.
1.8. Sketch functions and inverses
- Use sketch graphs to show the relationship between a function and its inverse.
- Understand that each graph is the reflection of the other in the line y = x.
Objective notes
8 learning objectivesConceptIGCSE Additional Math