Let's analyze the graph and answer the questions provided.

1. $f(-1)$

To find $f(-1)$, we look at the y-coordinate of the point where $x = -1$. From the graph, at $x = -1$, $y = 3$. Therefore, $f(-1) = 3$.

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

The limit of $f(x)$ as $x$ approaches $-1$ from the left. From the graph, as $x$ approaches $-1$ from the left, $f(x)$ approaches $3$. Therefore, $\lim_{x \to -1^-} f(x) = 3$.

3. $\lim_{x \to -1^+} f(x)$

The limit of $f(x)$ as $x$ approaches $-1$ from the right. From the graph, as $x$ approaches $-1$ from the right, $f(x)$ also approaches $3$. Therefore, $\lim_{x \to -1^+} f(x) = 3$.

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

Since both the left-hand limit and the right-hand limit as $x$ approaches $-1$ are equal and both are $3$, the limit of $f(x)$ as $x$ approaches $-1$ exists and is $3$. Therefore, $\lim_{x \to -1} f(x) = 3$.

To summarize, the answers are:

1. $f(-1) = 3$
2. $\lim_{x \to -1^-} f(x) = 3$
3. $\lim_{x \to -1^+} f(x) = 3$
4. $\lim_{x \to -1} f(x) = 3$

Would you like any further details or have any questions about these solutions? Here are some related questions you might find useful:

1. What are the definitions of left-hand limit and right-hand limit?
2. How do we determine if a limit exists at a point?
3. What is the difference between a limit and a function value at a point?
4. Can a function be discontinuous at a point where its limit exists?
5. How do you identify and interpret discontinuities in a graph?

Tip: Always compare the left-hand and right-hand limits at a point to determine if the overall limit exists.