Functions And Models

Four Ways to Represent A Function

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


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

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

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

A symbol that represents a number in the range of f$f$ 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$x$ would be the item that you put into a machine called f$f$ and ,y$y$ would be the new object that the machine gives you back.