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We are given a piecewise function:

\[
f(x) = 
\begin{cases} 
7x - 6 & \text{if } x < 0 \\
7x - 12 & \text{if } x \geq 0
\end{cases}
\]

Now, let's evaluate the function for the given values:

1. **\( f(-1) \)**: Since \(-1 < 0\), we use the first part of the function \( f(x) = 7x - 6 \).
   \[
   f(-1) = 7(-1) - 6 = -7 - 6 = -13
   \]
   So, \( f(-1) = -13 \).

2. **\( f(0) \)**: Since \(0 \geq 0\), we use the second part of the function \( f(x) = 7x - 12 \).
   \[
   f(0) = 7(0) - 12 = 0 - 12 = -12
   \]
   So, \( f(0) = -12 \).

3. **\( f(2) \)**: Since \(2 \geq 0\), we again use the second part of the function \( f(x) = 7x - 12 \).
   \[
   f(2) = 7(2) - 12 = 14 - 12 = 2
   \]
   So, \( f(2) = 2 \).

### Final Results:
- \( f(-1) = -13 \)
- \( f(0) = -12 \)
- \( f(2) = 2 \)

Would you like any further clarifications or details?

Here are 5 related questions:
1. How do we identify which piece of a piecewise function to use for a given input?
2. What happens if the function was defined differently for \( x = 0 \)?
3. Can a piecewise function have more than two pieces?
4. How do we graph a piecewise function like this one?
5. What are some real-life applications of piecewise functions?

**Tip:** Always check the boundary conditions in a piecewise function to ensure you use the correct piece of the function based on the input.

Given the piecewise function f(x) = {7x - 6 if x < 0, 7x - 12 if x >= 0}, calculate the values for f(-1), f(0), and f(2).

Learn how to solve a piecewise function for different values. The function f(x) is defined as f(x) = 7x - 6 for x < 0 and f(x) = 7x - 12 for x >= 0. This example includes solutions for f(-1), f(0), and f(2). Suitable for students in Grades 8-10.

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