The plot of f(x) at integer x already traces out an “S‐shaped” curve—slowly rising in the middle and steep at the ends. If you were to graph f for every real x, instead of just drawing isolated dots, you would draw a single continuous curve through those points with the following features:
• It is strictly increasing for all x.
• Around x≈−2 up to x≈3 it is relatively flat (small slope).
• As x→−∞ and x→+∞ it becomes steeper, so the tails rise more sharply.
• The result is a smooth “S‐shape” passing through all the blue dots.
In other words, replace the discrete dots by a smooth increasing curve interpolating them—shallow through the centre and steep towards the left and right ends—producing a continuous S‐shaped graph.