The Domain of a relation is the set of all possible values which can be used for the input of the independent variable (x).

The Range of a relation is the set of all possible values of the output of the dependent variable (y).

The Domain and Range can be found by listing the inputs and outputs.

Ordered pairs

(1,2), (0,5), (3,8), (5,9) (-3,2)

Domain: {-3, 0, 1, 3, 5}

Range: {2, 5, 8, 9}

An Arrow Diagram

D: {2, 4, 6, 8}

R: {1, 3, 5}

Graph

D: {-1, 0, 3, 4}

R: {5, 0, 2, 1}

D: {x E R}

R: {y E R}

D:  {x|-4 ≤ x ≤4, x ∈ R}

D: [-4, 4]

R: {y|0 ≤ y ≤ 5, y ∈ R}

R: [0, 5]

 

A comparison between two sets of elements is called a relation.

Relations can be represented

In Words

“The cost, C, of driving a car is related to the speed, s, at which it is driven.”

A Table of Values

A Set of Ordered Pairs

(20,10)

(30,9.1)

(40,8.4)

A Mapping or Arrow Diagram

An Equation 

C = – 0.14s + 12.4

A Graph

Independent Variable represents the inputs

The Corresponding Value – Dependent Variable represents the outputs

In an ordered pair, the values of the first coordinate are the independent values. The value of the second coordinate is therefore the dependent value.

Usually, the first given number in a table of values is the independent value, to the left of above the values of the following number, the dependent value.

In a mapping diagram, the arrows go from the independent value to the dependent value.

In a graph, the horizontal axis (x-axis) has the independent values, and the vertical axis (y-axis)  is the dependent values.

In an equation, usually, the dependent variable is isolated on the left side.