The graph provided shows a polynomial function $f(x)$. To determine the end behavior of the function, we focus on how the graph behaves as $x \to \infty$ and $x \to -\infty$.

From the graph, we can observe the following:

• As $x \to \infty$, $f(x) \to \infty$.
• As $x \to -\infty$, $f(x) \to \infty$.

This suggests that the polynomial is of even degree with a positive leading coefficient, since both ends of the graph rise upwards.

Thus, the end behavior of $f(x)$ can be described as:

• $f(x) \to \infty$ as $x \to \infty$
• $f(x) \to \infty$ as $x \to -\infty$

Would you like further details on polynomial behavior or any clarification on end behavior concepts?

Here are some related questions to explore further:

1. How can we determine the degree of a polynomial from its graph?
2. What impact does the leading coefficient have on the shape of a polynomial graph?
3. What is the significance of turning points in the graph of a polynomial?
4. How does the multiplicity of roots affect the behavior of a polynomial at those points?
5. What is the difference in end behavior between even and odd degree polynomials?

Tip: For polynomial functions, the degree and leading coefficient primarily determine the end behavior.