## Precalculus (6th Edition) Blitzer

For a polynomial function of degree 20, we have the end behavior of either $x\to\pm\infty, y\to\infty$ or $x\to\pm\infty, y\to-\infty$, which means that the curve rises or falls on both the left and right sides. For this reason, if the curve crosses the x-axis, it must return and cross the x-axis again; in other words, it can not cross the x-axis exactly once.