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Let's solve the piecewise function step by step, starting with \( f(-3) \).

The function \( f(x) \) is defined as:

\[
f(x) = 
\begin{cases} 
1 - x & \text{if } x < -1 \\
-x & \text{if } -1 \leq x \leq 6 \\
5x & \text{if } x > 6 
\end{cases}
\]

For \( f(-3) \):
- Since \( -3 < -1 \), we use the first case of the piecewise function: \( f(x) = 1 - x \).
- Substituting \( x = -3 \):

\[
f(-3) = 1 - (-3) = 1 + 3 = 4
\]

Thus, \( f(-3) = 4 \).

Let me know if you'd like to proceed with the other parts or have any questions!

Here are some related questions:
1. What is \( f(2) \) using the piecewise function?
2. What would \( f(7) \) be?
3. How do you determine which case to use for \( f(x) \) in a piecewise function?
4. Can piecewise functions have overlapping intervals for \( x \)?
5. How do piecewise functions relate to real-world scenarios?

**Tip:** When evaluating piecewise functions, always check the condition for \( x \) before substituting.

For the following piecewise-defined function, find (a) f(-3), (b) f(2), (c) f(4), and (d) f(7). f(x) = { 1 - x if x < -1, -x if -1 ≤ x ≤ 6, 5x if x > 6 }

Learn how to solve a piecewise-defined function. This example evaluates f(x) = { 1 - x if x < -1, -x if -1 ≤ x ≤ 6, 5x if x > 6 } for the values f(-3), f(2), f(4), and f(7). Suitable for high school students studying algebra.

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