Looking at the graph you've provided, I can see that we need to find the limits of the function as $x$ approaches 3 from the left (denoted as $\lim_{x \to 3^-}$), from the right (denoted as $\lim_{x \to 3^+}$), and the overall limit as $x$ approaches 3 (denoted as $\lim_{x \to 3}$).

Let's break it down:

1. $\lim_{x \to 3^-}$: This is the limit as $x$ approaches 3 from the left side (values less than 3).

   • As $x$ approaches 3 from the left, the y-value is approaching 4.

2. $\lim_{x \to 3^+}$: This is the limit as $x$ approaches 3 from the right side (values greater than 3).

   • As $x$ approaches 3 from the right, the y-value is also approaching 4.

3. $\lim_{x \to 3}$: This is the overall limit, which exists only if both the left-hand limit and the right-hand limit are the same.

   • Since $\lim_{x \to 3^-} = \lim_{x \to 3^+} = 4$, we conclude that $\lim_{x \to 3} = 4$.

Summary:

• $\lim_{x \to 3^-} = 4$
• $\lim_{x \to 3^+} = 4$
• $\lim_{x \to 3} = 4$

Let me know if you would like more details or if you have any questions!

Here are 5 related questions for deeper understanding:

1. What is the definition of a limit from the left and from the right?
2. How do we determine if the limit at a point exists?
3. What happens if the left-hand and right-hand limits are not equal?
4. Can a function have a limit at a point if it is not continuous at that point?
5. How does the concept of limits relate to derivatives in calculus?

Tip: When graphing limits, always check both the left and right approaches to ensure consistency!