# Functions, Graphs, and Limits

# Power Functions vs. Polynomials

In the world of horse races, power functions like 2^{x} will always grow faster than plain old polynomials, no matter how high the degree of the polynomial. By "grow faster'' we mean that if we go far enough to the right on the graph, the power function will be on top of the polynomial. We also mean that

and

.

If a function has a power function term in it, we consider it a power function for now.

Now we'd better correct a little something: we could have a power function getting more and more negative instead of more positive. We could also have a polynomial getting more negative instead of positive. It's important to take signs into consideration when determining this limit, because we could have