How to Determine if a Relation Is a Function
To determine if a relation is a function, you start by looking closely at how the inputs and outputs are paired. A relation is any set of ordered pairs, a rule, or a mapping that relates one quantity to another. Worth adding: the big question is simple: does each input have exactly one output? If the answer is yes, the relation is a function. If even one input has more than one output, then the relation is not a function.
This is the bit that actually matters in practice Simple, but easy to overlook..
What Is a Relation?
A relation is a broad mathematical idea. It can be shown as a list of ordered pairs, a table, a graph, or an equation. This leads to every relation has two sets of numbers or values: the domain and the range. Also, the domain is the set of all possible inputs, often shown as the x-values. The range is the set of all resulting outputs, often shown as the y-values Most people skip this — try not to..
As an example, the relation could be written as:
(1, 2), (2, 4), (3, 6)
Here, the domain is 1, 2, and 3, while the range is 2, 4, and 6. And this relation is not automatically a function just because it is a relation. It becomes a function only if each input has one clear output.
What Is a Function?
A function is a special type of relation. Consider this: in a function, every input in the domain is paired with exactly one output in the range. The output can be the same for two different inputs, but the same input cannot have two different outputs Simple as that..
The formal definition says that a function from a set A to a set B is a relation in which each element of A is related to exactly one element of B. The function notation
