I just want to get a better grasp of this concept. I don't think you can, for example $F(x) = 1000x$.
If I want to be within $1000$ of $f(x)$, i.e. $\epsilon = 1000$, then $\delta$ would be $250$.
So, $f(249) = 249,000$ - which is not within $1,000$ of $x$, if $x = 1$.
Is this correct?