Functions And Models

Four Ways to Represent A Function

What is a function?
A function $f$ is a rule that assigns to each element $x$ in a set $D$ exactly one element, called $f(x)$,in a set $E$


We usually consider functions for which the sets $D$ and $E$ are sets of real numbers.

The $D$ is called the domain of the function.
The number $f(x)$ is the value of $f(x)$ is the value of $f$ at $x$ and is read “$f$ of $x$”

The range of $f$ is the set of all possible values of $f(x)$ as $x$ varies throughout the domain.
A symbol that represents an arbitrary number in the domain of a function of $f$ is called and independent varialbe.

A symbol that represents a number in the range of $f$ is called a dependent variable.


There are four possible way to represent a function:
verbally (by a description in word)
numerically(by a table of values)
visually(by a graph)
algebraically(by an explicit formula)

So we can consider a function as a machine.
In that way ,$x$ would be the item that you put into a machine called $f$ and ,$y$ would be the new object that the machine gives you back.