what is this sort of function called? I am doing an assignment but I do not know how to do this problem. I have the following:
$$
f(x)=
\begin{cases}
0 & \text{for $x<0$},\\
x & \text{for $x\geq 0$}.
\end{cases}
$$
We are meant to determine whether it is continuous or not. I do not know why there is like a bracket with a $0$ up top and an $x$ at the bottom, nor do I understand what is meant by for $x \geq 0$. Basically, I do not understand the whole thing. What is this sort of function called so I can do some research on it (I plan to look it up on khan academy)?  

This function may be defined as $f\colon\Bbb R\to\Bbb R$,
$$f(x)=\mathrm{max}(0,x).$$
It is $f(x)=x$ for all $x$ greater or equal to $0$, hence it is $f(x)=0$ for $x=0$.
It is continuous in $0$ (check the definition of continuity for real functions of one real variable), hence it is continuous over all $\Bbb R$: before $0$ it is a constant function and after $0$ it is the identity function.
The derivative $f'(x)$ is not continuous in $0$ instead.
