Question

So I'm doing polynomial functions right now and it's talking about changes in direct of the graphs. Just wondering, is it possible to have more than 3-4 changes in direction on a single line? I've messed around trying to get a really squiggly, continuous line with one function on Desmos and nothing works.

Answer 1

increasing the order of the highest order term
should result in more "squiggles"

y = a x ... line

y = a x^2 ... parabola ... one direction change

y = a x^3 ... two changes

etc.

Answer 2

y = (x-c1)(x-c2)...(x-cn)
with n factors has n-1 changes in direction