Example ELF.NEL.1 :  Estimate $e$ using $e \approx (1+ \frac 1 n)^n$ for large values of $n$.

The following GeoGebra applet uses $n=2^k$.
Martin Flashman, Jan. 21, 2014. Created with GeoGebra

In the GeoGebra application, $e \approx (1+ \frac 1 {2^k})^{2^k}$. Notice how the arrows on the mapping diagrams are paired with the points on the graph.
You can use the slider to move the point for $k$ on the mapping diagram to see how the function value for the estimate for $e$ changes both on the diagram and on the graph.