The problem asks about the end behavior of the function $f(x)$ based on its graph.

Understanding End Behavior:

End behavior describes how the function behaves as $x$ approaches $+\infty$ (positive infinity) or $-\infty$ (negative infinity). For polynomial functions, this behavior is primarily determined by the leading term of the polynomial (the term with the highest degree).

Analyzing the Graph:

1. As $x$ approaches $+\infty$:

   • The graph appears to move downward. This means $f(x)$ decreases towards negative infinity.

2. As $x$ approaches $-\infty$:

   • The graph also moves downward, indicating $f(x)$ decreases towards negative infinity on this side as well.

Conclusion:

The end behavior of the function can be described as:

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

This behavior is typical of a polynomial function with an even degree and a negative leading coefficient.

Would you like any more details or have any questions about this? Here are five related questions to consider:

1. What types of functions typically exhibit this kind of end behavior?
2. How does the degree of a polynomial affect its end behavior?
3. How can you determine the leading coefficient of a polynomial function from its graph?
4. What are the differences in end behavior between even and odd degree polynomials?
5. How can end behavior help you identify the general shape of a function?

Tip: Always check both the leading coefficient and the degree of a polynomial to accurately predict its end behavior.