https://file.aiquickdraw.com/mathbot/file/1725998926146v8b3hvdd.jpg

Let's analyze the graph and solve problems 2 to 9 by interpreting the given limits and function values:

### 2. \(\lim_{{x \to 2}} f(x)\):
- From the graph, as \(x\) approaches 2 from both sides, \(f(x)\) seems to approach \(2\). 
  \[
  \lim_{{x \to 2}} f(x) = 2
  \]

### 3. \(\lim_{{x \to 4}} f(x)\):
- As \(x\) approaches 4 from both sides, the function stays at \(f(x) = 2\).
  \[
  \lim_{{x \to 4}} f(x) = 2
  \]

### 4. \(f(4)\):
- At \(x = 4\), the function value is \(2\).
  \[
  f(4) = 2
  \]

### 5. \(\lim_{{x \to 2^+}} f(x)\):
- As \(x\) approaches 2 from the right, \(f(x)\) approaches 2.
  \[
  \lim_{{x \to 2^+}} f(x) = 2
  \]

### 6. \(\lim_{{x \to 2^-}} f(x)\):
- As \(x\) approaches 2 from the left, \(f(x)\) also approaches 2.
  \[
  \lim_{{x \to 2^-}} f(x) = 2
  \]

### 7. \(\lim_{{x \to 6^-}} f(x)\):
- As \(x\) approaches 6 from the left, \(f(x)\) approaches 1.
  \[
  \lim_{{x \to 6^-}} f(x) = 1
  \]

### 8. \(\lim_{{x \to 6^+}} f(x)\):
- As \(x\) approaches 6 from the right, \(f(x)\) approaches 0.
  \[
  \lim_{{x \to 6^+}} f(x) = 0
  \]

### 9. \(f(6)\):
- At \(x = 6\), the graph shows that \(f(6) = 0\).
  \[
  f(6) = 0
  \]

Let me know if you'd like further clarification or more details! Here are some related questions to explore:

1. How do

Solve 2-9 based on the given graph of the function f(x).

Analyze the graph of the function f(x) to solve limits and continuity problems, including right-hand and left-hand limits at various points such as x = 2, 4, and 6. Suitable for students in Grades 10-12.

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