# Functions

A function is way to describe the relation between a set of inputs and a set of outputs.

For example, the price of one piece of chocolate is $2, two pieces of chocolate cost $4, three pieces of chocolate cost $6 and so forth.

The relation between quantity and price can be expressed with the linear function:

where x describes the quantity of chocolate, and f(x) describe the total price.

So f(x) is a way of expressing that f(x) depends on x. If you change x, then the outcome f(x) will change as well.

f(x) is often denoted by y:

f(x) = y

## Definition of a function

To each input x in a function there is one and only one assosiated element y.

## Concepts related to functions

There are a lot of concepts concerning functions. Here are a few of them:**Graph**

A graph is a depiction of a function. It is all the points (x,f(x)) or (x,y) drawn within a coordinate system. **Domain**

The domain is the set of numbers that can go in to a given function. It’s all valid values of x.

Example of how the domain of a function is denoted: **Codomain**

The codomain is the set of numbers which comes out of the function, when the valid values of x are put in to it.

Example of how the codomain of a function is denoted: **Extreme values of a function**

The minimum value and the maximum value of a function is respectively the lowest and the greatest value that can come out of the function.**Growth**

The outcome y increases, when x increases.**Decay**

The outcome y decreases, when x decreases.

## Graph drawer

Please enter a function, the graph of which you want to draw, and select the maximum and minimum of the input interval.Examples of how to enter different types of functions:

Proportional function: 1.5*x

Linear function: 2*x-3

Quadratic function: 2*x^2-3*x-4

Inversely proportional function: 2/x

Exponential function: 2*3^x

Power function: 2*x^3