# Functions

Functions

A function **accepts zero or more values**, performs some set of operations on them, and **returns one value** as the result. The **values **accepted by the function are called the **parameters**, or **arguments **of the function. Almost all functions have at least one parameter (pi() is one exception).

Lingo provides many functions, such as **power()**,** sin()**, **log()**, and **abs()**. If you write a handler that **returns a value**, it operates as a function. Also, in this tutorial any set of operations that you perform with a variable will be called a function of that variable. For example, **“x + 2”** is a function of **x**. In math you would write **“f(x) = x + 2”**.

When a function f(x) is graphed, the line or curve that is drawn is the **set of points (x, y)**, where y = f(x).

Types of Functions

The common types of functions in this tutorial are linear, polynomial, trigonometric, and parametric.

A **linear function** can be simplified to the form **ax + b**, where **a** and **b** are constants. When a linear function is graphed, it is a straight line. This is the most common type of function used and the most important to understand. Finding the right linear function for a particular need is described in Shifting & Scaling Numbers.

In a **polynomial function**, the variable is raised to some power. An example is**x ^{2} + 5**. There may be many terms of

**x**raised to different powers in the function. The graph of a polynomial function is a curve.

The **trigonometric functions** used in this tutorial are **sin()**, **cos()**, and **atan()**, which are described in Sine & Cosine Definitions. They are useful in parametric animation for creating **circular paths** and **oscillating motion** in general. In incremental animation they are used to find the **x and y components of a direction** (angle).

**Parametric functions** are a special type of function. In the first three types, the graphs consist of points **(x, f(x))**. But in parametric functions, the graph consists of points **(f(p), g(p))**, where f and g are other functions (non-parametric) and **p** is a parameter with a defined range. **p** is often associated with **time**. So a parametric function consists of several parts.

This parametric function **consists of three parts**: **f(p)**, **g(p)**, and **p:0->1**. f(p) is a combination of linear and trigonometric functions, and g(p) is a linear function.

Parametric functions are the idea behind parametric animation. Not only location, but all properties being animated are each a function of the parameter.

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