It seems you're describing a piecewise function. However, the function is not fully clear due to some missing symbols. Based on what I can infer, the function could look like this:

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

Would this be the correct interpretation of the function you're working with?

If so, here's a breakdown:

1. \( f(x) = 0 \) for \( x \leq 1 \) (this condition overlaps, so the value would be \(0\) in this case).
2. \( f(x) = x + 1 \) for \( -1 < x \leq 1 \).
3. \( f(x) = 0 \) for \( x > 1 \).

### Further Clarifications:
1. Is the boundary at \(x = 1\) included in multiple cases?
2. Should there be specific values for \(x = -1\) or \(x = 1\)?

If this matches what you intended, I can solve or further analyze it. Would you like me to plot or analyze the continuity of this function?

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Here are 5 related questions:
1. What happens to the function at \(x = -1\)? Is it continuous there?
2. What does the graph of this function look like over the interval \([-2, 2]\)?
3. How would the function behave if we modified the middle section, say making it \(f(x) = x^2\)?
4. Can this piecewise function be rewritten as a single equation using absolute values?
5. What is the derivative of this function in the intervals where it is non-constant?

**Tip:** Always check the boundaries in piecewise functions to ensure proper continuity and behavior at those points.

f(x) = {(0, x <= 1), (x + 1, -1 < x <= 1), (0, x > 1)}

Explore the behavior of a piecewise function defined by different rules across intervals. This example covers key concepts such as continuity at boundary points and piecewise function representation. Ideal for students in Grades 10-12.

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