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To find \( f(-1) \) from the piecewise function:

\[
f(x) = 
\begin{cases} 
2x + 8 & \text{for } -5 \leq x < -1 \\
-6 & \text{for } x = -1 \\
x + 5 & \text{for } -1 < x \leq 2
\end{cases}
\]

We are specifically asked to find \( f(-1) \). According to the second part of the piecewise definition, when \( x = -1 \), the function value is:

\[
f(-1) = -6
\]

Therefore, \( f(-1) = -6 \).

Would you like a detailed explanation of how to handle similar piecewise functions or explore another aspect of this problem?

Here are some related questions:
1. How do you graph a piecewise function like this one?
2. What is the domain and range of the given piecewise function?
3. How do you determine continuity at \( x = -1 \) for this function?
4. Can we evaluate \( f(x) \) for any other value of \( x \)?
5. How would the function change if the intervals were different?

**Tip:** Always check the intervals carefully when evaluating piecewise functions to ensure you're using the correct expression!

Find f(-1) for the given piecewise function.

Learn how to evaluate f(-1) for a piecewise function. This problem covers key algebraic concepts like function evaluation and working with intervals. Suitable for students in Grades 9-12.

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