# Is there a name for these type of functions (“defined by braces”)?

I often see functions that are defined in a way, as I like to call it using braces. For example:
$$f(x) = \begin{cases} g(x) & a \leq x \leq b\\ h(x) & a>x \lor b<x\\ \end{cases}$$
where $a$, $b$ are constants and $g(x)$, $h(x)$ are some random functions that depend on $x$.
(Note that they don't need to be functions, they can also be constants).

Is there any special name for this type of functions that are defined in this way?

• A constant is a function....the constant function if you will – Triatticus Jan 4 '18 at 22:24
• @Triatticus well...I learned two things today :) – Plexus Jan 4 '18 at 22:30