Study Notes
The domain and range of a function are fundamental concepts in mathematics, representing the set of possible inputs and outputs, respectively.
- Domain — the set of all possible values of the first variable in a function. Example: For the relation R = {(1, 2), (2, 2), (3, 3), (4, 3)}, the domain is {1, 2, 3, 4}.
- Range — the set of all possible values of the second variable in a function. Example: For the relation R = {(1, 2), (2, 2), (3, 3), (4, 3)}, the range is {2, 3}.
- Function Notation — a symbolic representation of a function, often written as f(x) = y. Example: f(x) = x^2.
- Mapping Diagram — a visual representation showing how each element of the domain is paired with an element in the range. Example: A diagram showing inputs mapped to outputs like a flow chart.
Exam Tips
Key Definitions to Remember
- Domain: The set of all possible input values (x-values).
- Range: The set of all possible output values (y-values).
- Function Notation: A way to represent functions using symbols like f(x).
Common Confusions
- Confusing domain with range.
- Misunderstanding one-to-one and many-to-one mappings.
Typical Exam Questions
- What is the range of f(x) = 2x - 3 for the domain {0, 1, 2}? Answer: { -3, -1, 1 }
- Write down the range of h(x) = x^2 for -3 ≤ x ≤ 6. Answer: {0, 1, 4, 9, 16, 25, 36}
- What is the range of f(x) = x^2 for -3 ≤ x ≤ 6? Answer: {0, 1, 4, 9, 16, 25, 36}
What Examiners Usually Test
- Ability to identify and state the domain and range.
- Understanding of function notation and mapping diagrams.
- Application of domain and range concepts in different functions.