hi im new but i''ll try to help, please correct me if i am wrong.

Q1.Would you explain How to determine the equation of the function?

A. you were given a set points and expected to deduce an equation that would out put those values, it looks like there is a pattern so i think this is a geometric sequence problem.

Q2.what does it mean to determine the sign of the function in each interval "created by zeros"of the function?

A. the Zeros of a function are the x values where y=0, that is where the curve of the function intersects the x axis. anything above the x axis is + and below is -. The curve looks like an odd function which means it is flipped across x axis for negative x values.

With these given points:

(-12,-30888), (-10,-12375), (-8,-4032), (-6,-945), (-4,-120), (-2,-3), (0,0), (2,3), (4,120), (6,945), (8,4032), (10,12375), (12,30888)

i cant remember how to do geometric sequences but i'll help on Q2.

with the points you were given, it again looks like f(x) = - f(-x) but im not sure until you figure the equation. y= 0 is a zero, that occurs at x=0 so x= 0 is a 'root' or a 'zero' this splits the graph into two intervals, where if x>= 0 then the sign is positive, and if x< 0 the sign is negative.

a hint on Q1. it looks like its in the form of ax^n where a,n are + integers

thats all i can help you with