Let's examine the graph to evaluate the given statement: $\lim_{x \to 2^-} f(x) = 4$.

• The notation $\lim_{x \to 2^-} f(x)$ represents the left-hand limit of the function $f(x)$ as $x$ approaches 2 from the left.
• To determine this, we need to observe the behavior of the function $f(x)$ as $x$ approaches 2 from values less than 2.

From the graph:

• As $x$ approaches 2 from the left (i.e., from values less than 2), the function appears to approach the value $f(x) = 2$, not $f(x) = 4$.

Thus, the statement $\lim_{x \to 2^-} f(x) = 4$ is false.

Would you like more details or have any further questions?

Here are 5 related questions to deepen understanding:

1. What is the right-hand limit of $f(x)$ as $x \to 2^+$?
2. How do you determine the overall limit $\lim_{x \to 2} f(x)$?
3. What is the value of the function $f(x)$ at $x = 2$?
4. How can we interpret the open and closed circles on the graph in terms of