TITLE: what is this sort of function called?
QUESTION [9 upvotes]: 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)?

REPLY [6 votes]: just to be pedantic, there is no such thing as a "piecewise function", i.e. "piecewise" doesn't name a class of functions but rather a way to simply describe functions by case distinction. Every function (that can be described anyhow) can be (trivially) described as "piecewise" e.g. the function $f:\mathbb{R}\to \mathbb{R}$ with $f(x)=x^2$ could written as
$$
f(x)=\begin{cases}
      x^2\text{    if } x<0\\
      x^2 \text{   otherwise} 
     \end{cases}
$$
I think what causes trouble with such descriptions is the fact that most beginners in math do think of functions as some kind of "algebraic term with variables" and not of abstract objects that could be described in many ways..