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To determine the limits from the graphs provided in your image, we'll analyze each one based on how the function behaves as \( x \) approaches a specific value.

### 1. \( \lim_{x \to 2} f(x) \) 
For the first graph:
- As \( x \) approaches 2 from the left (\( x \to 2^- \)), the function \( f(x) \) decreases toward \( -\infty \).
- As \( x \) approaches 2 from the right (\( x \to 2^+ \)), the function \( f(x) \) increases toward \( +\infty \).
- **Conclusion:** The limit does not exist because the left-hand limit and right-hand limit are not equal.

### 2. \( \lim_{x \to 1} g(x) \)
For the second graph:
- As \( x \) approaches 1 from the left (\( x \to 1^- \)), the function \( g(x) \) approaches 1.
- As \( x \) approaches 1 from the right (\( x \to 1^+ \)), the function \( g(x) \) also approaches 1.
- **Conclusion:** The limit exists and is equal to 1.

### 3. \( \lim_{x \to 3} h(x) \)
For the third graph:
- As \( x \) approaches 3 from the left (\( x \to 3^- \)), the function \( h(x) \) approaches \( 2 \).
- As \( x \) approaches 3 from the right (\( x \to 3^+ \)), the function \( h(x) \) approaches \( -2 \).
- **Conclusion:** The limit does not exist because the left-hand limit and right-hand limit are not equal.

### 4. \( \lim_{x \to 0} j(x) \)
For the fourth graph:
- As \( x \) approaches 0 from the left (\( x \to 0^- \)), the function \( j(x) \) approaches \( -1 \).
- As \( x \) approaches 0 from the right (\( x \to 0^+ \)), the function \( j(x) \) approaches \( -1 \).
- **Conclusion:** The limit exists and is equal to \( -1 \).

Would you like any further details or explanations on these solutions?

Here are five related questions to deepen your understanding:
1. What is the formal definition of a limit?
2. How do one-sided limits differ from two-sided limits?
3. Can you have a limit that exists even if the function is not defined at that point?
4. How do vertical asymptotes affect the existence of limits?
5. What is the significance of limits in calculus?

**Tip:** Always check the behavior of the function from both sides of the point to determine whether a limit exists and whether it is finite or infinite.

Explore how to find limits from graphs with detailed examples. Learn about one-sided limits, infinite limits, and the concept of limit existence. Suitable for high school and college-level students studying calculus and graph analysis.

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