A Continuous Compactly Supported Function on $\mathbb{R}^n$ is Uniformly Continuous

Let $n\ge1$ be a natural number, let $\lVert\,\cdot\,\rVert$ be the Euclidean norm on $\mathbb{R}^n$, and let $d$ denote the Euclidean distance, a metric on each Euclidean space.

Let $g:\mathbb{R}^n\to\mathbb{R}$ be continuous on $\mathbb{R}^n$, as a map from $(\mathbb{R}^n,d)$ to $(\mathbb{R},d)$, and compactly supported.

Then $g$ is uniformly continuous on $\mathbb{R}^n$.