Algebra 15 - Functions

The lecture introduces functions as a special type of binary relation, explaining how they map elements from a domain to a range, with each input having exactly one output. It covers the concepts of domain, range, and codomain, and provides examples using favorite fruits to illustrate valid and invalid functions. The lecture also discusses the graphical representation of functions as ordered pairs, often visualized on a Cartesian plane.

What is a function in the context of binary relations?

How does a function differ from a general binary relation?

What is meant by the domain of a function?

Explain the concept of codomain and how it relates to the range of a function.

Provide an example of a function and describe its domain, codomain, and range.

What conditions must be met for a binary relation to be classified as a function?

How can functions be represented graphically, and what does this representation indicate?