It looks like you uploaded an image showing a calculus problem that involves limits and a function $f(x)$. Here's how we can work through the steps:

1. Analyze the Problem:

   • The goal is to calculate:
     • $\lim_{x \to -4^-} f(x)$ (limit as $x$ approaches $-4$ from the left),
     • $\lim_{x \to -4} f(x)$ (overall limit as $x$ approaches $-4$),
     • $f(-4)$ (value of the function at $x = -4$, if defined).

2. Table of Values:

   • You need to input values close to $-4$ (e.g., $-4.1$, $-4.01$, $-3.99$, $-3.9$, etc.) into the table to compute $f(x)$.
   • Use these values to evaluate $f(x)$ and observe the trend for left-hand and right-hand limits.

3. Solution Steps:

   • Check the limit from the left $(x \to -4^-):$ Calculate $f(x)$ for values slightly less than $-4$.
   • Check the limit from the right $(x \to -4^+):$ Calculate $f(x)$ for values slightly greater than $-4$.
   • Determine if the left-hand and right-hand limits are equal; if they are, the limit $\lim_{x \to -4} f(x)$ exists.
   • Finally, determine $f(-4)$ based on the function's definition at $x = -4$.

If you provide the function $f(x)$ or its definition (or example values for testing), I can guide you further or solve it step-by-step.

Let me know how you'd like to proceed! Here are some related questions to help you think further:

1. What trends do you observe in $f(x)$ as $x$ approaches $-4$ from the left and the right?
2. Does the function appear continuous at $x = -4$?
3. Is the left-hand limit equal to the right-hand limit at $x = -4$?
4. What happens if $f(x)$ is undefined at $x = -4$? How does this affect the answer?
5. What tools (calculator, graphing software) can be used to visualize the function's behavior near $x = -4$?

Tip: Always check for discontinuities or undefined points in the function when working with limits and direct evaluation!