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The given function \( f(x) \) is defined as a piecewise function:

\[
f(x) = 
\begin{cases}
2x - 1 & \text{if } x < 1 \\
-x + 3 & \text{if } x \geq 1 
\end{cases}
\]

We need to evaluate \( f(x) \) at different values.

1. **\( f(-4) \)**: Since \( -4 < 1 \), we use the first piece of the function, \( f(x) = 2x - 1 \):
   \[
   f(-4) = 2(-4) - 1 = -8 - 1 = -9
   \]

2. **\( f(-2) \)**: Since \( -2 < 1 \), we use the first piece again:
   \[
   f(-2) = 2(-2) - 1 = -4 - 1 = -5
   \]

3. **\( f(1) \)**: Since \( 1 \geq 1 \), we use the second piece of the function, \( f(x) = -x + 3 \):
   \[
   f(1) = -(1) + 3 = -1 + 3 = 2
   \]

4. **\( f(4) \)**: Since \( 4 \geq 1 \), we use the second piece again:
   \[
   f(4) = -(4) + 3 = -4 + 3 = -1
   \]

The values are:
\[
f(-4) = -9, \quad f(-2) = -5, \quad f(1) = 2, \quad f(4) = -1
\]

Would you like more details or have any questions?

Here are some related questions to explore further:
1. How would you graph this piecewise function?
2. What is the domain and range of \( f(x) \)?
3. How does changing the function to \( f(x) = 2x + 1 \) for \( x < 1 \) affect the outputs?
4. Can you find where the function \( f(x) \) equals zero?
5. What are the properties of piecewise functions that make them useful for modeling real-life situations?

**Tip:** When working with piecewise functions, always pay attention to the conditions for each piece to determine which expression to use.

f(x) is defined as a piecewise function: f(x) = 2x - 1 if x < 1 and f(x) = -x + 3 if x ≥ 1. Find f(-4), f(-2), f(1), and f(4).

Learn how to evaluate the piecewise function f(x) = 2x - 1 for x < 1 and f(x) = -x + 3 for x ≥ 1 at different points. This solution explains step-by-step how to calculate f(-4), f(-2), f(1), and f(4). Suitable for students in Grades 9-10.

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