Graph Function: What Does It Mean?

[Monk1]

View attachment 5251

What does the function even mean?

 

[MarkFL]

That is one way to denote the floor function, more commonly given as \(\displaystyle \lfloor x \rfloor\), which means the largest integer not greater than $x$. Its value at $x$ is called the integral part or integer part of $x$. The fllor function may be defined by the set equation:

\(\displaystyle \lfloor x \rfloor=\max\{m\in\mathbb{Z}\,|\,m\le x\}\)