Intervallfunktioner

An intervallfunktion, or interval function, is a function where the domain is an interval of real numbers and the range is also an interval of real numbers. This means that for any two points within the domain interval, their corresponding output values will cover all real numbers between the minimum and maximum of those output values.

A key property of intervallfunktioner is that they are typically continuous. If a function is continuous on a closed interval [a, b], then its range will also be a closed interval [m, M], where m is the minimum value and M is the maximum value the function takes on that interval. This is a consequence of the Intermediate Value Theorem.

Intervallfunktioner are fundamental in calculus and analysis. They describe phenomena that change smoothly over a continuous range. Examples include the temperature over a day, the position of a moving object, or the growth of a population over time, assuming these changes are continuous. The concept helps in understanding the behavior and properties of functions over specific continuous segments of the real number line.