The problem asks for the limit of the function $f(x)$ as $x$ approaches $-1$, based on the graph provided.

Looking at the graph:

• For values of $x$ approaching $-1$ from the left (i.e., $x \to -1^-$), the graph approaches $y = 6$.
• For values of $x$ approaching $-1$ from the right (i.e., $x \to -1^+$), the graph also approaches $y = 6$.

Since both the left-hand limit and right-hand limit are equal and approach $y = 6$, we conclude that:

$\lim_{{x \to -1}} f(x) = 6$

Do you have any further questions, or would you like additional details on limits? Here are some related questions you might find useful:

1. What is the definition of a limit in calculus?
2. How do one-sided limits work, and how are they related to two-sided limits?
3. Can a function have a limit if there is a discontinuity at that point?
4. How can you visually identify the limit from a graph?
5. What are common mistakes when evaluating limits graphically?

Tip: Always check both the left-hand and right-hand limits when determining if the limit exists.