Summary and Exam Tips for Functions
Functions is a subtopic of Functions, which falls under the subject Mathematics in the IB DP curriculum. A function is a special type of relation where each element in set is associated with exactly one element in set . This is denoted as . If an element in maps to multiple elements in , it is not a function. The domain of a function is the set of all possible inputs, while the range is the set of all possible outputs. For example, the domain of is all real numbers, and its range is .
Composite functions involve combining two functions, and , to form a new function . One-to-one (injective) functions map each element of to a unique element of , while onto (surjective) functions cover every element in . An inverse function reverses the mapping of a function, denoted as , and exists only for one-to-one functions. For instance, if , its inverse is .
Exam Tips
- Understand Definitions: Make sure you grasp the definitions of functions, domain, range, and types of functions (one-to-one, onto).
- Practice Problems: Work through examples of finding domains and ranges, especially for functions involving fractions and square roots.
- Composite Functions: Practice forming and breaking down composite functions to understand their components.
- Inverse Functions: Learn to find inverse functions and verify them using .
- Graphical Understanding: Use graphs to visualize functions, especially to determine if they are one-to-one or onto.
