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The problem you're working on seems to focus on **finding limits numerically and graphically** based on the graph provided for the function \( f(x) \). Here’s a breakdown of how to approach this:

The graph shows the behavior of the function \( f(x) \) around certain values. The limits to be found are likely referring to points around \( x = 2 \), \( x = 4 \), and \( x = 6 \), as visible in the graph.

Let me help you go through these steps:

### 1. **Identify the Limits on the Graph**
    - **\( \lim_{x \to 2} f(x) \)**: Look at the graph near \( x = 2 \). Does the function approach a specific value from both the left and the right?
    - **\( \lim_{x \to 4} f(x) \)**: Do the same near \( x = 4 \).
    - **\( \lim_{x \to 6} f(x) \)**: Observe the behavior near \( x = 6 \).

### 2. **Interpreting the Graph**
    - **For \( x = 2 \)**: Check whether the left-hand limit and the right-hand limit approach the same value.
    - **For \( x = 4 \)**: Similarly, observe if the function has a jump or approaches the same value from both sides.
    - **For \( x = 6 \)**: Inspect the graph's behavior at \( x = 6 \).

### 3. **Special Points**
    - The presence of any discontinuities, holes, or jumps in the graph can change the value of the limit.
  
Would you like me to analyze each limit individually based on the graph, or would you prefer further explanation on limits? Here are a few additional related questions you might find useful.

### 5 Related Questions:
1. What is the difference between one-sided limits and two-sided limits?
2. How do discontinuities in a function affect the calculation of limits?
3. What does it mean if a function has no limit at a certain point?
4. How do you interpret a vertical asymptote when determining limits?
5. What is the connection between limits and the derivative of a function?

**Tip:** When analyzing limits graphically, always check for behavior from both sides of the point to confirm if the limit exists!

Finding Limits Numerically and Graphically based on the graph of the function f(x)

Explore how to find limits both numerically and graphically by analyzing the behavior of a function f(x) around certain values. This problem covers key concepts of limits, continuity, and the interpretation of graphical behavior. Suitable for Grades 11-12 or Calculus 1 students.

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