The Function Concept
Definition of a function, domain, codomain, image, equality of functions, and the graph.
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Learning Objectives
- State the definition of a function \(f \colon A \to B\).
- Identify the domain, codomain, and image of a given function.
- Distinguish a function from a rule that violates existence or uniqueness.
- Read and sketch graphs of functions in the Cartesian plane.
- Determine when two functions are equal.
About This Course Unit
We formalise the notion of function, starting from the intuition built in the Sequences course, and introduce the vocabulary that the rest of the course depends on.