# Ordered Pairs

Ordered pairs are considered to be a fundamental part as far as graphing is considered. Ordered pairs are important to plot various functions on the graph and ordered functions when plotted on graph will determine how the function looks like on the graph.

## What is an ordered pair?

An ordered is determined as a set of outputs and inputs and are used to indicate the relationship between two different values. A set of these inputs and outputs is called a relation and a relation with one output for each of the inputs is called a function.

An ordered pair is known to be represented as (INPUT, OUTPUT).

Ordered pairs have an important role to play for recognizing relations and the implications of various functions while we proceed to understand ordered pairs, we would need to understand about relations and functions too.

## What is a function?

Several relations are sensible while the others are not. Well, functions are the relations that are actually sensible. This is the fact why all functions can be called relations but not all relations can be termed as functions.

To understand it better, a function can be termed as a relation which indicates and describes that there can and should be only one output for each input. It could also be said that a special set of ordered pairs or a relation that follows a rule. This would mean that one value x is eligible to be associated with only one value y.

For example, consider the below mentioned value of x that can be related to one value y. Here, in the above example domain is the input value (x) and range is the output value (y) i.e. (x,y).

Similarly, In the above example also, one value of x is associated with one value of y.

## Graphing Function

Using the inputs and outputs that have been listed in the table or relation, points could be easily plotted on a coordinate grid. Using a graph of the data points, it becomes easy to determine whether a relation is a function or not. This can be done by the vertical line test. If a vertical line drawn through the graph touches only one point, that relation is a function. Take a look at the below graph of the relation map. If a vertical line is drawn through it, it would touch only one plotted point. And this probably determines that it is a function.

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