Special name for a function

Question

Suppose we define the function $L(x)$ as follows: $$\begin{equation} L(x)= \begin{cases} 0, & \text{if}\ x<0 \\ x, & \text{if}\ 0<x<1 \\ 1, & \text{otherwise}. \end{cases} \end{equation}$$

For example, suppose we have $x_i(t+1)=x_i(t)+1$, then we can write $x_i(t+1)=L[y_i(t)]$, where $y_i(t)=x_i(t)+1$.

Does the function $L(x)$ have a special name? Is it similar to an operator?

Thank you for any help.

Answer 1

$L$ is the CDF of the uniform distribution.

When you limit yourself to $(0,1)$, it is the identity function.

Answer 2

I call $L(x)$ a ramp function, based on the picture it produces. It's not really that special of a name.