A mathematical function is a relation that uniquely associates each input with exactly one output. Functions can be represented in various forms, including equations, graphs, and tables. They are fundamental in mathematics, allowing us to model relationships between quantities and solve problems across different fields. Functions can be classified into different types, such as linear, quadratic, and exponential. Each type has distinct characteristics and applications. For example, a linear function represents a straight line, while a quadratic function forms a parabola. Understanding these functions is essential for advanced studies in mathematics and its applications in science and engineering.