# Function

A function has different meanings based on the context.

In scientific text, it is common to come across sentences along the lines:

The plot displays Y as a function of X

_{1}, X_{2}, and X_{3}.

This has the same meaning as Y is dependent on the independent variables X_{1}, X_{2}, and X_{3}.

## Calculus

In traditional calculus a function is defined as a relation between two terms called variables because their values vary. Call the terms *x* and *y*. If every value of *x* is associated with exactly one value of *y*, then *y* is said to be a function of *x*; *x* can only one-to-one relationships, however *y* can have one-to-many relationships (different values of *x* can be associated with *y*). It is customary to call *x* the *independent variable*, and *y* the *dependent variable* because its value depends on *x*.

Letters at the end of the alphabet are traditionally applied to variables, and letters elsewhere in the alphabet (usually first letters such as *a*,*b*,*c*,...) are applied to constants. Constants are terms in an equation that have a fixed value. they remain the same as *x* and *y* vary.