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:
A graph is a depiction of a function. It is all the points (x,f(x)) or (x,y) drawn within a coordinate system.
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:
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.
The outcome y increases, when x increases.
The outcome y decreases, when x decreases.