Chapter 3, Polynomial and Rational Functions - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 301: 1

Graph II represents a polynomial function.

In order to be a polynomial function, the graph must be a smooth and continuous line. There can be no sharp points/corners, and there can be no breaks or gaps in the line. With this, we can eliminate graphs I, III, and IV. This leaves us with graph II as the best representation of a polynomial function.