The graph shown in the image represents the graph of a polynomial function.

Here’s why:

• A polynomial function has a smooth and continuous curve, meaning it doesn't have any breaks, gaps, or sharp corners.
• The graph in the image meets this criterion; it is smooth, continuous, and does not have any discontinuities or sharp points.
• Additionally, polynomial functions have end behavior where the function either increases or decreases without bound as $x$ approaches positive or negative infinity. In the graph, as $x$ goes to infinity or negative infinity, the graph flattens out, which is typical of polynomial functions, particularly even-degree ones or those with large powers that dominate the behavior at the extremes.

Would you like further details on polynomial functions or the specific behavior seen in this graph?

Follow-up questions:

1. What are the main characteristics of polynomial functions?
2. How can you determine the degree of a polynomial from its graph?
3. What is the significance of the turning points in polynomial graphs?
4. How does the end behavior of a polynomial function relate to its degree?
5. How can the roots of a polynomial be determined from its graph?

Tip:

The number of turning points in a polynomial function's graph is at most one less than the degree of the polynomial.