Let's go through the problem one by one based on the graph provided:

(a) $f(-3)$

• From the graph, when $x = -3$, the value of the function $f(x)$ is clearly 4.
• Answer: $f(-3) = 4$

(b) $\lim_{x \to -3} f(x)$

• As $x$ approaches -3 from both sides, the function appears to approach 4. Since the function is continuous at $x = -3$, the limit exists.
• Answer: $\lim_{x \to -3} f(x) = 4$

(c) $f(-1)$

• At $x = -1$, the graph shows that the value of $f(x)$ is 3.
• Answer: $f(-1) = 3$

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

• As $x$ approaches -1 from both sides, the function smoothly approaches 0, even though $f(-1)$ itself is 3. Therefore, the limit as $x \to -1$ is 0.
• Answer: $\lim_{x \to -1} f(x) = 0$

(e) $f(2)$

• At $x = 2$, the graph shows that the value of $f(x)$ is 0.
• Answer: $f(2) = 0$

(f) $\lim_{x \to 2} f(x)$

• As $x$ approaches 2 from both sides, the function approaches the value 1. So, the limit exists and is 1, even though $f(2)$ is 0.
• Answer: $\lim_{x \to 2} f(x) = 1$

(g) $f(4)$

• At $x = 4$, the graph shows that the value of $f(x)$ is 5.
• Answer: $f(4) = 5$

(h) $\lim_{x \to 4} f(x)$

• As $x$ approaches 4 from both sides, the function smoothly approaches 5. So, the limit as $x \to 4$ is 5.
• Answer: $\lim_{x \to 4} f(x) = 5$

Would you like a detailed explanation of any specific part of this solution, or do you have any further questions?

Here are 5 related questions:

1. What is the definition of a limit in calculus?
2. How can a function's value differ from its limit at a specific point?
3. What does it mean for a function to be continuous at a point?
4. What are one-sided limits, and how do they relate to overall limits?
5. How do piecewise functions affect limits?

Tip: When analyzing limits, it's important to check both the left-hand and right-hand behavior of the function near the point of interest. This ensures that the limit exists and is consistent.