Theory of Functions

The theory of functions is a branch of mathematics that studies relationships between inputs and outputs. A function assigns each input exactly one output, which can represent various real-world situations. For example, consider a vending machine: when you select a button (input), it dispenses a specific item (output). Functions are essential for modeling and analyzing changes in systems across different fields, such as physics, economics, and engineering. They help us understand how different factors influence one another and are foundational for advanced concepts in mathematics and science.