The graph in the image you provided depicts a function with asymptotes at $x = -2$ and $x = 2$, and it shows the general behavior of the graph as $x$ approaches extreme values in both the positive and negative directions.

End Behavior of the Graph:

• As $x \to -\infty$, the graph approaches $y = 0$, indicating the function approaches a horizontal asymptote at $y = 0$.
• As $x \to +\infty$, the graph similarly approaches $y = 0$, showing the same horizontal asymptote at $y = 0$.

Vertical Asymptotes:

• There are vertical asymptotes at $x = -2$ and $x = 2$. As $x$ approaches these values from either side, the graph rises or falls to infinity.

This function has key characteristics of rational functions or hyperbolic functions with vertical asymptotes and horizontal end behavior.

Would you like more details on the function's specific behavior, or are you interested in understanding the calculation behind these observations?

Here are some related questions:

1. What is the formula of a rational function that would match this graph?
2. How do vertical asymptotes affect the end behavior of a function?
3. What is the significance of horizontal asymptotes in the end behavior of rational functions?
4. How can you find the vertical asymptotes of a rational function algebraically?
5. What is the difference between horizontal and oblique asymptotes?

Tip: The end behavior of a function often reveals a lot about its asymptotic nature and can help predict how the graph behaves at extreme values of $x$.