Assignment:
If you have an arbitrary polynomial P(x) of the nth degree in x, and you graph the equation y = P(x), describe the overall shape of this graph. What happens when x gets large in the positive and negative directions, and how many peaks and valleys does the graph have? How many times does the graph cross the x-axis? (To simplify, let the sign of the highest power term in P(x) be positive.)
Provide complete and step by step solution for the question and show calculations and use formulas.