Question

In relation to polynomial functions what does the graph look like when the leading coefficient is positive and the degree is odd?

Answer 1

The graph of an odd-degree polynomial function with a positive leading coefficient will have its left end heading downwards and the right end heading upwards, creating an 'S' or 'C' shaped curve.

Step-by-step explanation:

When the graph of a polynomial function has a positive leading coefficient and the degree is odd, the ends of the graph go in opposite directions.

Specifically, the left end will head downwards, and the right end will head upwards. This is due to the nature of odd-degree polynomial functions which are symmetric with respect to the origin, causing this characteristic 'S' or 'C' shaped curve when plotted.

As the degree of the polynomial gets higher, the graph might have more turns, but the overall behavior at the ends remains consistent with the aforementioned pattern.