This problem involves determining the behavior of a function $f(x)$ as $x \to -\infty$ and $x \to \infty$. The goal is to evaluate the limits:

1. $\lim_{x \to -\infty} f(x)$
2. $\lim_{x \to \infty} f(x)$

To solve this, you need to:

1. Input various values for $x$ into the table.
2. Use the corresponding $f(x)$ values to observe the trends as $x \to -\infty$ and $x \to \infty$.

Would you like assistance with specific values for $x$ to test in this case? If you share more about $f(x)$, I can help predict its behavior and guide you through the calculation. Let me know how I can assist further!

Related Questions:

1. What are the general methods for finding the limits of functions as $x \to \pm\infty$?
2. How can trends in a function's table help predict its end behavior?
3. What does it mean if a limit "does not exist" ($DNE$) at infinity?
4. How can graphing a function help verify limit calculations?
5. What are common functions whose limits at infinity are undefined or infinite?

Tip: Always check for symmetry or patterns in $f(x)$ as you input values—it might simplify limit evaluation.