Let $n$ be a very large positive integer.
Let $f \in\mathbb{R}\rightarrow\mathbb{R}$ be a continuous function, satisfying $0\leq f\leq1$, and supported on $[-n,-\frac{1}{n}]\cup[\frac{1}{n},n]$ such that $f(x)=1$ for every $x\in[-n+\frac{1}{n},-\frac{2}{n}]\cup[\frac{2}{n},n-\frac{1}{n}]$.
That is, at $x=-n$, $f$ quickly rises from $0$ to $1$, drops back to zero between $-\frac{2}{n}$ to $-\frac{1}{n}$, is zero at $[-\frac{1}{n},\frac{1}{n}]$, rises back to $1$ from $\frac{1}{n}$ to $\frac{2}{n}$, and quickly drops back to zero again at $x=n-\frac{1}{n}$.
How does the Fourier transform of such function look?