The graph you've shared appears to be that of a polynomial function. To determine its end behavior, we look at the direction of the graph as $x$ approaches $\infty$ and $-\infty$.

From the image, we can observe the following:

• As $x \to \infty$ (moving towards the right), the graph goes upwards, meaning $f(x) \to \infty$.
• As $x \to -\infty$ (moving towards the left), the graph also goes upwards, meaning $f(x) \to -\infty$.

This behavior suggests a polynomial with an odd degree (since it crosses from one end to another) and a positive leading coefficient, such as $x^3$ or $x^5$ with a positive leading term.

So, the end behavior can be summarized as:

$\text{As } x \to \infty, \, f(x) \to \infty$ $\text{As } x \to -\infty, \, f(x) \to -\infty$

Would you like more details or have any questions about polynomial end behavior?

Here are some questions related to this topic:

1. What are the common end behaviors of different polynomial degrees?
2. How can the sign of the leading coefficient affect the end behavior?
3. How do we determine the degree of a polynomial from a graph?
4. How does end behavior differ in even- and odd-degree polynomials?
5. How can we confirm if this is indeed a polynomial graph?

Tip: The end behavior of a polynomial function depends only on its leading term; all other terms become insignificant as $x$ approaches $\pm \infty$.