We explain what a mathematical function is, how it can be expressed, its variables, the types that exist and other characteristics.
What is a mathematical function?
A mathematical function (also simply called a function) is the relationship between one magnitude and another, when the value of the first depends on the second.
For example, if we say that the value of the temperature The day depends on the time at which we consult it, we will be without knowing it establishing a function between both things. Both magnitudes are variables, but they are distinguished between:
- Dependent variable. It is the one that depends on the value of the other magnitude. In the case of the example, it is the temperature.
- Independent variable. It is the one that defines the dependent variable. In the case of the example it is the hour.
In this way, every mathematical function consists of the relationship between an element of a group A and another element of a group B, provided that they are uniquely and exclusively linked. Therefore, this function can be expressed in algebraic terms, using signs as follows:
f: A → B
a → f (a)
Where TO represents the domain of the function (F), the set of starting elements, while B is the codomain of the function, that is, the arrival set. For fa) the relation between an arbitrary object is denoted to belonging to the domain TO, and the only object of B that corresponds to him (his image).
These mathematical functions can also be represented as equations, using variables and arithmetic signs to express the relationship between the quantities. These equations, in turn, can be solved, solving their unknowns, or else be graphed geometrically.
Types of mathematical functions
Mathematical functions can be classified according to the type of correspondence that occurs between the elements of domain A and those of B, thus having the following:
- Injective function. Any function will be injective if elements other than the domain TO correspond to elements other than B, that is to say, that no element of the domain corresponds to the same image of another.
- Surjective function. Similarly, we will speak of a surjective (or subjective) function when each element of the domain TO corresponds to an image in the B, even if it means sharing images.
- Bijective function. It occurs when a function is injective and surjective at the same time, that is, when each element of TO corresponds to a single element of B, and there are no unassociated images in the codomain, that is, there are no elements in B that do not correspond to one in A.