Existence of Smooth Bump Functions on Euclidean Space

Let $n\in$ $\mathbb{N}$, let $x_0$ be a point of Euclidean space $\mathbb{R}^n$, and let $r,s\in\mathbb{R}$ with $0<r<s$. Then there exists a smooth map $\chi:\mathbb{R}^n\to\mathbb{R}$ such that, with $d$ denoting the Euclidean distance on $\mathbb{R}^n$:

1. $0\le\chi(x)\le 1$ for every $x\in\mathbb{R}^n$;
2. $\chi(x)=1$ for every $x\in\mathbb{R}^n$ with $d(x,x_0)\le r$;
3. $\chi(x)=0$ for every $x\in\mathbb{R}^n$ with $d(x,x_0)\ge s$.