What is the meaning of $(−\infty, \infty]$?

Question

What is the meaning of this mathematical notation for a function $$f : \mathbb{R}^n \to (−\infty, \infty]$$ Especially I am wondering the left bracket and right square bracket?

Answer 1

$(-\infty,\infty]$ is an interval of the extended real line. It contains all the real numbers as well as the $\infty$ symbol, but does not contain the $-\infty$ symbol.

In other words, a values of the function $f$ will be either a real number or the special symbol $\infty$. What the properties of $\infty$ are here, other than counting as larger than every real number, must be understood from the context.