These types of functions are vey important to understand. They describe how the function preserves distinctness, and how the functions interact with both the codomain and the domain.

###### Injective

An injective function is a function that whenever *one to one.*

Example 1:

Consider the function *f* is not an injective function. A numerical example would be

Example 2:

Now consider the linear function

###### Surjective

A surjective function is a function from *onto* functions.

Example 1:

Let *f* maps to all non negative numbers in

###### Bijection

A function that is both Injective and Surjective is called a bijection.

Example:

Let

###### Non Bijective Functions

There are some functions that are neither Injective nor Surjective.

Example:

Let *0* and *1* both map to *0*. Therefore it isn’t injective. *f(x)* doesn’t hit all of the integers in the codomain, for example for *f(x)=1* *x * must be $latex *\frac{1}{2} (1\pm\sqrt{5})\not\in\mathbb{Z} $*