piecewisefunktio

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the main function's domain. In simpler terms, it's a function that behaves differently on different parts of its input range. Imagine a graph that is made up of several distinct line segments or curves, each representing a different formula for a specific section of the x-axis.

For example, a common piecewise function might be defined as:

f(x) = x^2 if x < 0

f(x) = 2x if 0 <= x < 3

f(x) = 6 if x >= 3

This means that for any input less than zero, the function squares the input. For inputs between zero (inclusive) and three (exclusive), it doubles the input. For inputs greater than or equal to three, the function's output is always six.

The "pieces" of a piecewise function are the individual sub-functions, and the "intervals" are the specific ranges of the input variable (often denoted by x) to which each sub-function applies. The points where the intervals meet are called boundary points. It is important that for a function to be well-defined, the sub-functions must agree on the value at these boundary points if the interval is inclusive of that point.

Piecewise functions are used in various fields of mathematics, science, and engineering to model real-world phenomena that exhibit different behaviors under different conditions. Examples include modeling pricing structures, analyzing motion with changing speeds, or describing electrical signals.