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Based on the provided image, you need to determine the limits for the given functions as they approach specific values of \(x\). Let’s analyze each graph to find the limits.

### 1. \(\lim_{x \to a^-} f(x)\)
- **Interpretation**: This represents the limit of the function \(f(x)\) as \(x\) approaches \(a\) from the left.
- **Graph**: The function appears to approach a certain value as \(x\) gets close to \(a\) from the left. From the graph, it looks like as \(x\) approaches \(a\) from the left, the function value approaches a certain \(y\)-value.
- **Result**: \(\lim_{x \to a^-} f(x) = L\), where \(L\) is the \(y\)-value the function approaches.

### 2. \(\lim_{x \to a^+} f(x)\)
- **Interpretation**: This represents the limit of the function \(f(x)\) as \(x\) approaches \(a\) from the right.
- **Graph**: The graph shows that as \(x\) approaches \(a\) from the right, the function approaches a different \(y\)-value.
- **Result**: \(\lim_{x \to a^+} f(x) = M\), where \(M\) is the \(y\)-value the function approaches.

### 3. \(\lim_{x \to a} f(x)\)
- **Interpretation**: This represents the limit of the function \(f(x)\) as \(x\) approaches \(a\) from both sides.
- **Graph**: The limit exists if the left-hand limit and right-hand limit are equal. If they are not equal, the limit does not exist.
- **Result**: 
  - If \(L = M\), then \(\lim_{x \to a} f(x) = L = M\).
  - If \(L \neq M\), then \(\lim_{x \to a} f(x)\) does not exist.

### 4. \(\lim_{x \to b} f(x)\)
- **Interpretation**: This is similar to the previous problem, where you must determine the limit as \(x\) approaches \(b\).
- **Graph**: Examine the graph near \(x = b\) and check if the function approaches the same value from both the left and the right.
- **Result**: Again, if the left-hand limit equals the right-hand limit, the limit exists and is equal to this common value.

### 5. \(\lim_{x \to c} f(x)\)
- **Interpretation**: This is the limit as \(x\) approaches \(c\).
- **Graph**: Like the previous cases, analyze if the function approaches the same value from both directions near \(x = c\).
- **Result**: Determine whether the left and right-hand limits are equal or not, and conclude whether the limit exists.

If you provide specific points \(a\), \(b\), and \(c\), I can help with exact limit values. 

Would you like more detailed explanations or have any questions? Here are five relative questions to expand this concept:

1. What happens to the limit if the graph has a jump discontinuity?
2. How do you determine the limit if the function is undefined at the point but approaches a value?
3. What is the significance of one-sided limits in determining the overall limit?
4. How would you find the limit if the function has an infinite discontinuity?
5. How can you graphically confirm that a limit does not exist?

**Tip**: Always check both the left-hand and right-hand limits separately before concluding the overall limit at a point.

Learn how to determine limits of functions from graphs. Explore one-sided limits, continuity, and discontinuities through detailed graph analysis. Suitable for high school and college students.

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