The end behavior of a polynomial function is determined by its degree and the sign of its leading coefficient, that is, the coefficient of the highest degree monomial. As $x$ approaches to infinity, a positive leading coefficient makes the graph extend upward, and a negative one makes the graph extend downward. For even-degree polynomials, the left-end behaves the same way as the right-end. For odd-degree polynomials, they have opposite behavior.

In the figure, the $3$rd and $6$th degree polynomials must have negative leading coefficients, as their right-ends extend downward. The rest have right-ends that extend upward, so they have positive leading coefficients. Notice that the higher degree polynomial functions have more turns. While a higher degree doesn't necessarily imply more turns, it increases the number of turns the graph could have.