How can a function have multiple outputs?

Question

Quoting Wikipedia (from this page)-

Functions with multiple outputs are often written as vector-valued functions.

How is it possible for a function to give multiple outputs?

Answer 1

One such function is $f: \Bbb R \to \Bbb R^2\\ x \to (3x+2,4x-1)$

It is important to note that when one says multiple outputs, it is not that there are several alternative outputs, there is a set or ordered sequence of outputs. You can view the output as a single sequence or as several numbers. When you talk of multiple outputs you are viewing it as several numbers. When you talk about a vector valued function, you view the output as one sequence. That is the spirit of the comments you have received.

Answer 2

Suppose I wanted to define a "function" that takes a real number as input and returns two things: the input rounded down and the input rounded up. Strictly speaking, a function should only return one value. I can "cheat" however by defining the function $f: \mathbb{R} \rightarrow \mathbb{Z} \times \mathbb{Z}$ where $f(x) = (\lfloor x \rfloor, \lceil x \rceil)$. Since $f$ takes a real number as input and gives a single ordered pair as output, we are still respecting the definition of a function.