What conjectures/predictions can you make about polynomial functions whose highest exponent is 6, or 7?
degree 6: maximum of 6 real roots. Exactly 6 roots, if you include complex values.
shape is basically a steep parabola, with possible wiggles along the bottom somewhere. May open up or down.
It will have an absolute minimum/maximum somewhere.
Degree 7: at least one real root, total of 7 roots, including comples ones.
because of odd degree, will have a range of -oo to +oo.