Nonnegative function ($f(x)\ge 0$)

A real-valued function $f:X\to \mathbb{R}$ is nonnegative when $f(x)\ge 0$ for every input $x\in X$. For example, $f(x)=x^2$ and $g(x)=|x|$ are nonnegative functions on the real line.

Products and nonnegative linear combinations preserve the property: if $f,g\ge 0$ and $\alpha ,\beta \ge 0$, then $f(x)g(x)\ge 0$ and $\alpha f(x)+\beta g(x)\ge 0$ at every point. A partition of unity uses nonnegative functions whose values sum to one, so its weighted combinations lie in the convex hull of the values being combined.