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The given piecewise function is:

\[
f(x) = 
\begin{cases} 
7x - 1 & \text{if } x < 0 \\
7x - 2 & \text{if } x \geq 0 
\end{cases}
\]

We need to calculate the values of \( f(-1) \), \( f(0) \), and \( f(2) \).

1. **Calculating \( f(-1) \):**

   Since \(-1 < 0\), we use the first part of the function: 

   \[
   f(-1) = 7(-1) - 1 = -7 - 1 = -8
   \]

2. **Calculating \( f(0) \):**

   Since \(0 \geq 0\), we use the second part of the function:

   \[
   f(0) = 7(0) - 2 = 0 - 2 = -2
   \]

3. **Calculating \( f(2) \):**

   Since \(2 \geq 0\), we use the second part of the function:

   \[
   f(2) = 7(2) - 2 = 14 - 2 = 12
   \]

### Final Answers:
- \( f(-1) = -8 \)
- \( f(0) = -2 \)
- \( f(2) = 12 \)

Would you like further explanations on these calculations, or do you have any other questions?

### Related Questions:
1. How do you determine which part of a piecewise function to use?
2. What happens if you input a value exactly at the boundary of a piecewise function?
3. How can you graph a piecewise function?
4. How do piecewise functions apply in real-world scenarios?
5. What are the common mistakes when evaluating piecewise functions?

### Tip:
Always double-check the conditions of a piecewise function to ensure you are using the correct formula for the given input value.

Given the function f(x) = { 7x - 1 for x < 0; 7x - 2 for x >= 0 }, calculate the following values: f(-1), f(0), f(2).

Learn how to evaluate a piecewise function for the values f(-1), f(0), and f(2) with detailed calculations. The function is defined as f(x) = 7x - 1 for x < 0 and f(x) = 7x - 2 for x >= 0. This algebra problem is suitable for students in Grades 7-10.

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