Many programs require a mathematical function capable of mapping an interval of numbers linearly onto another interval. A function maps one interval linearly onto another.

Example

The interval can be mapped to using .

Derivation

The function can be thought of as a linear function that passes through the points and . This means that the function should map to and to .

With two points the slope can be obtained and the function can be written and simplified.

The function can be verified to ensure a correct mapping of to .

The same can be done to ensure maps to .