Types of functions

A function It is a correspondence between two sets of elements, which occurs when each of the elements of the domain set is related to a single element of the range set. Where the elements of the domain set are never repeated.

There are different types of functions such as: injectives, surjectives y bijectives.

Injective function

A function is injective when each element in the domain has only one element in the range.

injective function

Recall that the domain and range of a function are graphically represented in the Cartesian system as the x-axis and the y-axis, the union of each element of the domain with the elements of the range graphically represent a point (x, y) (domain, range) . Joining these points we will have the graphic representation of a function. To graphically check whether a function is injective or not, lines are drawn parallel to the domain axis (the x axis). If they cut the function only at one point, then it is injective, otherwise (it cuts at more than one point) it is not. Example:

example of injection function

    non-injective function

Surjective function

A function is surjective if each element in its range (y axis), at least one domain element (x axis) belongs to it.

surjective function

To know graphically if a function is surjective, we must draw lines parallel to the x-axis and observe if they cut the function at least one point. Example:

Surjective function example

non-surjective function

 Bijective function

It is that function that is injective and surjective at the same timeOr, that is, each element of the domain has an element in the range and vice versa. From the previous examples the following graphs are bijective functions:

Bijective functions