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Let's analyze the given problem carefully.

### Given Information:
- **Student 1:** Represents the linear function as an equation: \( f(x) = 3x - 6 \)
- **Student 2:** Represents the function in a table with values:

  \[
  \begin{array}{|c|c|}
  \hline
  x & f(x) \\
  \hline
  -2 & -12 \\
  -1 & -9 \\
  0 & -6 \\
  1 & -3 \\
  2 & 0 \\
  \hline
  \end{array}
  \]

### Solution Analysis:

1. **Finding the Intercepts:**

   - **Equation from Student 1 (\( f(x) = 3x - 6 \)):**

     - **Y-intercept:**  
       The y-intercept occurs when \( x = 0 \):
       \[
       f(0) = 3(0) - 6 = -6
       \]
       So, the y-intercept is at \( (0, -6) \).

     - **X-intercept:**  
       The x-intercept occurs when \( f(x) = 0 \):
       \[
       3x - 6 = 0
       \]
       \[
       3x = 6
       \]
       \[
       x = 2
       \]
       So, the x-intercept is at \( (2, 0) \).

   - **Table from Student 2:**
     - From the table, when \( x = 2 \), \( f(x) = 0 \). This confirms that the x-intercept is at \( (2, 0) \).
     - When \( x = 0 \), \( f(x) = -6 \). This confirms that the y-intercept is at \( (0, -6) \).

2. **Evaluating the Statements:**

   - **Option A:**  
     "The equation of \( f(x) \) reveals an \( x \)-intercept at \( (2, 0) \), while the table for \( f(x) \) reveals a \( y \)-intercept at \( (0, -6) \)."
     
     This statement is **true** based on the calculations and values presented above.

   - **Option B, C, and D:**  
     All these options are false because they either mix up the intercepts or give incorrect points for the intercepts.

### Conclusion:
The correct answer is:
- **Option A:** The equation of \( f(x) \) reveals an \( x \)-intercept at \( (2, 0) \), while the table for \( f(x) \) reveals a \( y \)-intercept at \( (0, -6) \).

Would you like me to explain anything in more detail, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How do you determine the x-intercept of a linear equation given in standard form?
2. What is the slope of the function \( f(x) = 3x - 6 \), and how can it be interpreted?
3. How would the graph of \( f(x) = 3x - 6 \) look, and where would the intercepts be plotted?
4. What is the difference between x-intercepts and y-intercepts in any function?
5. How can you verify the intercepts of a function if only given its table of values?

**Tip:** To determine intercepts, set one variable to zero and solve for the other—this method works for both linear and non-linear functions.

Two students represent the same linear function, f(x). Student 1 correctly writes f(x) as an equation, while Student 2 correctly creates a table for f(x). Which statement is true?

Explore how to identify x- and y-intercepts of the linear function f(x) = 3x - 6 using both an equation and a table representation. This problem demonstrates key concepts in algebra, including finding intercepts and interpreting function tables, suitable for students in Grades 7-9.

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