Polynomial functions of degree 2 or more have graphs that do not have sharp corners; recall that these types of graphs are called smooth curves. Polynomial functions also display graphs that have no breaks. Curves with no breaks are called continuous. Figure 1 shows a graph that represents a **polynomial function** and a graph that represents a function that is not a polynomial.

### Example 1: Recognizing Polynomial Functions

Which of the graphs in Figure 2 represents a polynomial function?

### Solution

The graphs of *f* and *h* are graphs of polynomial functions. They are smooth and **continuous**.

The graphs of *g* and *k *are graphs of functions that are not polynomials. The graph of function *g* has a sharp corner. The graph of function *k* is not continuous.

### Q & A

**Do all polynomial functions have as their domain all real numbers?**

*Yes. Any real number is a valid input for a polynomial function.*