Based on my book
The rate of change of $f(u)$ as $u$ changes can be measured by looking at the change in $f$ between two values of $u$, divided by the change in $u$: $$\frac{Δf}{Δu} = \frac{f(u_2)-f(u_1)}{u_2-u_1}$$For a monotonic transformation, $f(u_2)-f(u_1)$ always has the same sign as $u_2-u_1$. Thus a monotonic function always has a positive rate of change. This means that the graph of a monotonic function will always have a positive slope, as depicted in Figure 4.1A.
Now what I don't understand is if the monotonic function is as simple as $f(u) = u +1$ (Changing it slightly from the non-monotonic function) how come it comes it will always have a positive rate of change compared to the non-monotonic function?