function: definition

Function: Definition

• A function is a correspondence from a first set, called the domain, to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range.

• Domain elements are called inputs.

• Range elements are called outputs.

The independent variable, x, denotes a member of the domain and the dependent variable, y, denotes a member of the range. We say, "y is a function of x".

Function: Definition

In this course the members of each set are real numbers. For now, x will represent a real number from the domain and y or f (x) will represent a real number from the range.

Function: Mapping Diagram Representation

A function may be represented using a set of ordered pairs (x, y), a table of values, an equation, a graph, and a mapping diagram.

Here is an example of a function represented by a mapping diagram.

5 17

0 2

- 2 - 4

The rules that govern the correspondence between the two sets are:

1. Multiply the domain value by three.

2. Add two to the result.

Function: Mapping Diagram Representation

Here, the left oval represents the domain. The right oval represents the range.

5 17

0 2

- 2 - 4

Here is the same function represented by a set of ordered pairs:

{ (- 2, - 4), (0, 2), (5, 17) }.

Function: Ordered Pairs

5 17

0 2

- 2 - 4

Function: Table Representations

5 17

0 2

- 2 - 4

Here is the same function represented by a table of values:

x y

- 2 - 40 2 5 17

Let’s say that the mapping is just a partial representation of infinitely many ordered pairs. Then here is the same function represented by an equation:

y = 3x + 2 or f (x) = 3x + 2.

Function: Equation

5 17

0 2

- 2 - 4

Function: Graph Representations

5 17

0 2

- 2 - 4

Here is the same function represented by a graph (orange line pictured).

Function