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 is an example of a piecewise function.
The big bracket means that the function is evaluated differently depending on what domain $x$ is in. 
When $x < 0$ then $f(x) = 0$.
When $x \geq 0$ then $f(x) = x$.
Continuous functions are functions that do not have any gaps. 
This function is continuous. 
An example of a function that is not continuous would be
$$
f(x)=
\begin{cases}
0 & x<0\\
1 & x\geq 0
\end{cases}
$$
This is not continuous because there is a gap between the line segments at $x = 0$.
