Real-valued functions

A real-valued function is a rule that assigns a single real number to each input from a specific set, typically numbers. For example, if the input is a number representing time, the function might give the temperature at that time as an output. These functions help describe relationships between quantities in nature, science, and engineering, allowing us to understand how one value depends on another. They are fundamental in mathematics for analyzing patterns, making predictions, and modeling real-world phenomena using precise numerical relationships.