TI-30X Pro MathPrint - How does num-solve work?

[wb.c]

I've been messing around with the TI-30X Pro MathPrint for a while now, and I was trying to understand how num-solve works exactly. It is well understood that the initial guess has an impact on the solution found, when there is more than one solution. Initially I thought that the solver must do a check of sorts to determine which direction it will step towards to find the solution.
   
This lead me to think that the solver must always do a validation of sorts to the right of the initial guess to determine if the results are getting smaller (closer to zero or smaller than the result from the initial guess). But it seems this is not the case, and I'm curious how this solver actually works.

Take for example now f(x)=0.6sin(x)-0.2x+1.
The results are quite interesting and not exactly what I expected.
The most interesting results are highlighted.

   
   

It seems that the upper and lower bounds did not have an impact on the result, other than excluding certain results and where the Error appeared. Where the Error appears, I would have expected to get the first result greater than the lower bound, as was seen with the first tabulated outcome. In this first outcome, any value greater than 10.8303 with the bounds outside of the solutions always results in the first solution (3.62). However, the same setup, but with the lower bound higher than the first solution but lower than the second one, did not produce the second solution as the result, it still gave the third solution (7.98).

Does anyone know how the TI-30X Pro MathPrint numeric solver functions?