To analyze the end behavior of the function $f(x)$ based on the graph:

1. As $x \to -\infty$: Observing the left side of the graph, as $x$ decreases towards negative infinity, the function $f(x)$ also goes downwards, moving towards $-\infty$.

2. As $x \to \infty$: Looking at the right side of the graph, as $x$ increases towards positive infinity, the function $f(x)$ moves upwards, tending towards $\infty$.

Thus, the correct end behavior is:

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

Answer:

The correct choice is:

• As $x \to -\infty$, $y \to -\infty$ and as $x \to \infty$, $y \to \infty$.

Would you like further details on why end behavior is determined this way?

Here are some follow-up questions to deepen understanding:

1. What are some typical patterns of end behavior for polynomial functions of different degrees?
2. How does the leading term in a polynomial function affect its end behavior?
3. What is the impact of even vs. odd degrees on the end behavior of polynomial functions?
4. Can end behavior be predicted without a graph for certain types of functions?
5. How does end behavior differ between polynomial and exponential functions?

Tip: Remember, for polynomials, the end behavior is heavily influenced by the highest power term.