# Is x^2+5 a function?

A function $f : X \setminus \to Y$ is given when you have two sets, and a law which tells you how to associate one, and only one item $y \setminus \in Y$ to each $x \setminus \in X$.
The simplest case is represented by numeric function, which means that you associate a real number to every real number. So yes, ${x}^{2} + 5$ is a function, because for every real number you can calculate its square, and then add five. This is exactly what the "law" I mentioned before tells you to do: writing $f \left(x\right) = {x}^{2} + 5$ (or also often $y = {x}^{2} + 5$) means "take a number $x$, multiply it by itself, obtaining ${x}^{2}$, and then add $5$ to the result, obtaining ${x}^{2} + 5$.