Let's analyze the graph of the function $f(x)$ and evaluate the limits based on the information given in the image.

Step-by-step Analysis

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

As $x$ approaches 3 from the left:

• The value of $f(x)$ is approaching 2.

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

As $x$ approaches 3 from the right:

• The value of $f(x)$ is approaching 3.

Since the left-hand and right-hand limits are not equal, the overall limit at $x = 3$ does not exist.

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

As $x$ approaches $-1$ from the left:

• The value of $f(x)$ is approaching 0.

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

As $x$ approaches $-1$ from the right:

• The value of $f(x)$ is approaching 1.

Since the left-hand and right-hand limits are not equal, the overall limit at $x = -1$ does not exist.

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

As $x \to 4$, there is a jump in the graph:

• From the left, $f(x) \to 3$.
• From the right, $f(x) \to 1$.

Since the left-hand and right-hand limits do not match, the limit does not exist.

Answer Summary