Unit 4

Function Rule

A function is a relationship in math between two variables, often x and y, and for every value of x there is exactly one value of y. The x value is referred to as the independent variable and the y as the dependent variable.

Function

A function is a special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/2 ("f of x is x divided by 2") is a function, because each input "x" has a single output "x/2": • f(2) = 1 • f(16) = 8 • f(−10) = −5

Mapping

In many branches of mathematics, the term map is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a continuous function in topology, a linear transformation in linear algebra, etc.

Input

function. close window. A function is any relationship between inputs and outputs in which each input leads to exactly one output. It is possible for a function to have more than one input that yields the same output. function machine.

Domain

All the values that go into a function The output values are called the range. Domain → Function → Range Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then {1,2,3,...} is the domain.

One-to-one correspondence

In mathematics, a bijection, bijective function or one-to-one correspondence is a function between the elements of two sets, where every element of one set is paired with exactly one element of the other set, and every element of the other set is paired with exactly one element of the first set.

Output

In modern mathematics, a function is defined by its set of inputs, called the domain; a set containing the set of outputs, and possibly additional elements, as members, called its codomain; and the set of all input-output pairs, called its graph.

Range

The set of all output values of a function. Domain → function → Range Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then its range is {1,4,9,...}

Vertical line test

The set of all output values of a function. Domain → function → Range Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then its range is {1,4,9,...}