The graph shown represents the function $f(x)$, and the question asks for the end behavior of this function. End behavior refers to what happens to the function's values (i.e., $y$) as $x$ approaches positive infinity ($x \to \infty$) or negative infinity ($x \to -\infty$).

From the graph:

• As $x \to -\infty$ (to the left), the graph of $f(x)$ goes upwards, meaning $y \to \infty$.
• As $x \to \infty$ (to the right), the graph of $f(x)$ decreases, heading downward, meaning $y \to -\infty$.

Therefore, the correct end behavior is:

• As $x \to -\infty$, $y \to \infty$
• As $x \to \infty$, $y \to -\infty$

The correct answer is: As $x \to -\infty$, $y \to \infty$ and as $x \to \infty$, $y \to -\infty$.

Would you like any further details on how end behavior is analyzed, or do you have any questions?

Here are 5 related questions to expand on this topic:

1. How do you determine the end behavior of polynomial functions from their degrees and leading coefficients?
2. What are horizontal asymptotes and how do they relate to end behavior?
3. Can rational functions have different end behavior compared to polynomials?
4. How do exponential functions behave as $x \to \infty$ or $x \to -\infty$?
5. What is the difference between end behavior and local behavior of a function?

Tip: Always look at the leading term of a polynomial to quickly determine its end behavior.