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I would like to formulate a bump function (link) $f(x)$ with the following properties on the reals:
$$
f(x) :=
\begin{cases}
0, & \mbox{if } x \le -1 \\
1, & \mbox{if } x = 0 \\
0, & \mbox{if } x \ge 1
\end{cases}
$$
In addition (because it's a bump function), it should be smooth and continuou...
