# Definition:Square/Function/Real

## Example of Real Function

The (real) square function is the real function $f: \R \to \R$ defined as:

$\forall x \in \R: \map f x = x^2$

### Graph

A graph of the square function on $\R$ can be presented as:

## Properties

### Real Square Function is not Injective

Let $f: \R \to \R$ be the real square function:

$\forall x \in \R: \map f x = x^2$

Then $f$ is not an injection.

### Real Square Function is not Surjective

Let $f: \R \to \R$ be the real square function:

$\forall x \in \R: \map f x = x^2$

Then $f$ is not a surjection.

## Also see

• Results about the square function can be found here.