I've resurrected a few nearly-defunct brain cells, and to the best of my memory, the thrust-N1 curve on a well-known engine goes something like this:
1) At low power - typical approach settings - the curve is approximately linear with a low dF/dN slope.
2) Near TO, the curve is again nearly linear with a high dF/dN slope.
3) There's smooth curve connecting the two linear segments.
Hope this make some sense - and that my memory isn't playing tricks on me.