The most conceptually simple answer must be to use programming instead of mathematics to add these two functions.
f[x_]:= Which[x<1, 100, x<2, 95, x<5, 80, ...]
g[x_]:=Sin[2 x^2]*x/4 + Sin[0.3 x] + (8/30)*x
h[x_]:=f+g
In terms of C-implementation, and efficiency, there could be some nonobvious solutions. For instance, convert the discrete function to a continuous function by making it piecewise linear, and then maybe using abs to make it a single expression. Then they can all be added together.
But to be more practical, you probably want to approximate. A linear fit works well enough possibly but you can try other functions too, e.g.,
Fit[{{0, 100}, {1, 95}, {5, 80}, {10, 70}, {15, 40}, {20, 25}, {25,
15}, {30, 10}}, {1, x, Sin[(Pi/15) x]}, x]
