The problem is asking to find $\lim_{x \to 1^{-}} f(x)$ using the given graph. This represents the limit of $f(x)$ as $x$ approaches 1 from the left.

To solve this:

1. Locate $x = 1$ on the graph (this is where the vertical line is closest to $x = 1$).
2. Focus on the behavior of the function as $x$ approaches 1 from the left-hand side ($x < 1$).
3. As $x$ gets closer to 1 from the left, the graph shows the function approaching a value of approximately $y = -5$.

Thus, $\lim_{x \to 1^{-}} f(x) = -5$.

Would you like further clarification or more details on this? Here are five related questions:

1. How is the limit defined for one-sided limits (from the left or right)?
2. What happens if the left and right limits differ at a point?
3. How do you calculate $\lim_{x \to 1^{+}} f(x)$ using the same graph?
4. What is the overall limit $\lim_{x \to 1} f(x)$, considering both sides?
5. How can limits be used to determine if a function is continuous at a point?

Tip: When dealing with one-sided limits, always check the graph's behavior specifically from the side indicated (left or right) for accuracy.