It looks like you've defined a piecewise function. Let me clarify it and express it properly:

\[
f(x) = 
\begin{cases} 
-2 & \text{if } x \leq -2 \\
-2x - 1 & \text{if } -2 < x \leq 1 \\
0 & \text{if } x > 1 
\end{cases}
\]

To break it down:

1. **For \( x \leq -2 \):** \( f(x) = -2 \)
2. **For \( -2 < x \leq 1 \):** \( f(x) = -2x - 1 \)
3. **For \( x > 1 \):** \( f(x) = 0 \)

If this is correct, let me know how you'd like to proceed! I can help you analyze this function further or perform operations like evaluating it at specific points, finding limits, or graphing it.

Would you like more details or clarifications?

Here are 5 possible related questions to explore:

1. How do you graph a piecewise function?
2. How do you find the domain and range of a piecewise function?
3. How would you compute the limit of this function as \( x \) approaches certain points (e.g., \( x = 1 \))?
4. How can we determine whether this function is continuous at \( x = -2 \) and \( x = 1 \)?
5. What does the derivative of this piecewise function look like?

**Tip:** For any piecewise function, it's important to check for continuity at the transition points where the pieces meet!

Explore how to define and analyze a piecewise function with conditions like f(x) = -2 for x <= -2, f(x) = -2x - 1 for -2 < x <= 1, and f(x) = 0 for x > 1. This detailed breakdown covers key concepts such as linear functions, inequalities, and continuity, suitable for high school students.

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