The piecewise function you've provided seems to have some inconsistencies in the intervals specified. Let's clarify the function based on typical piecewise function notation. Here's how it might be correctly interpreted:

\[
f(x) = \begin{cases} 
-1 & \text{for } -4 < x < 1 \\
x + 2 & \text{for } x < -5 
\end{cases}
\]

However, the intervals provided overlap and don't cover the entire number line. Specifically:

1. The interval \( -4 < x < 1 \) is a valid range where \( f(x) = -1 \).
2. The interval \( x < -5 \) doesn't overlap with the first interval, but leaves a gap between \( -5 < x \leq -4 \) and \( x = -5 \) itself. 

Would you like to clarify or add more intervals to the function, or should I proceed with solving based on the current interpretation?

Do you have any questions about this? Here are 5 follow-up questions to consider:
1. How would you define \( f(x) \) for values of \( x \) between \( -5 \) and \( -4 \)?
2. Should the function \( f(x) = x + 2 \) apply for values \( x < -4 \) instead of \( x < -5 \)?
3. Would you like to evaluate this function for specific \( x \) values?
4. Are you interested in graphing this piecewise function?
5. Do you need to understand how to solve a similar problem?

**Tip:** Always ensure that piecewise function intervals do not overlap and cover all possible values of \( x \) to define a function completely.

Explore the piecewise function f(x) = {-1 for -4 < x < 1, x + 2 for x < -5} with a detailed explanation and clarification. This problem involves analyzing piecewise functions, understanding interval notation, and addressing overlaps in function definitions. Suitable for Grades 11-12.

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