What is Function, domain, curve?

Example 11.10

Study $f(x) = \sqrt{x^2 + 1}$ on $\R$. The inner function $u(x) = x^2 + 1$ is positive, decreasing on $\intoc{-\infty}{0}$ and increasing on $\intco{0}{+\infty}$ (a shifted square). By point 3, $f$ has the same variations: decreasing then increasing, with minimum $f(0) = 1$.