From the graph you've uploaded, we can determine the end behavior by analyzing how the function behaves as $x$ approaches positive and negative infinity.

• As $x \to \infty$ (moving to the right), the graph of $f(x)$ decreases towards negative infinity, meaning $f(x) \to -\infty$.
• As $x \to -\infty$ (moving to the left), the graph of $f(x)$ increases towards positive infinity, meaning $f(x) \to \infty$.

This matches the following option from your choices:

• As $x \to \infty$, $f(x) \to -\infty$, and as $x \to -\infty$, $f(x) \to \infty$.

Let me know if you need further details or explanation! Here are five related questions for further exploration:

1. How do you determine the end behavior of polynomial functions in general?
2. What role do leading terms of polynomials play in defining end behavior?
3. How does the degree of a function affect its graph’s end behavior?
4. Can rational functions have similar end behavior to this graph?
5. How does symmetry (odd or even function) affect the end behavior of functions?

Tip: For polynomial functions, the degree and the sign of the leading coefficient provide a reliable way to predict the end behavior.