That's a proper function, a conformal mapping, etc.
A relation is a mapping or pairing of input values with output values.
An example of a relation that is not a function is the relation defined by the set of points {(1, 2), (1, 3), (2, 4), (3, 5)}. In this relation, the input value 1 corresponds to two different output values (2 and 3), violating the definition of a function, which states that each input must have exactly one output. Therefore, since one input maps to multiple outputs, this relation is not a function.
Relation
An ordered pair can represent either a relation or a function, depending on its properties. A relation is simply a set of ordered pairs, while a function is a specific type of relation where each input (first element of the pair) is associated with exactly one output (second element of the pair). If an ordered pair is part of a set where each input corresponds to only one output, it defines a function. Otherwise, it is just a relation.
cost or input
No, not every relation is a function. In order for a relation to be a function, each input value must map to exactly one output value. If any input value maps to multiple output values, the relation is not a function.
It's a type of function
It is a bijective function.
Is called "function".
A one-to-one or injective function.
function
A relation is a mapping or pairing of input values with output values.
An example of a relation that is not a function is the relation defined by the set of points {(1, 2), (1, 3), (2, 4), (3, 5)}. In this relation, the input value 1 corresponds to two different output values (2 and 3), violating the definition of a function, which states that each input must have exactly one output. Therefore, since one input maps to multiple outputs, this relation is not a function.
A relation is a function if every input has a distinct output.
Productivity
Relation
A one-to-one function, a.k.a. an injective function.