https://file.aiquickdraw.com/mathbot/file/1729876369070go35ubf3.jpg

The piecewise function you've provided can be described as:

\[
f(x) =
\begin{cases} 
x^2 - 1 & \text{for } x < 0 \\
-x + 2 & \text{for } 0 \leq x < 2 \\
2 & \text{for } x \geq 2
\end{cases}
\]

Let me know if you'd like to graph this function or have any further clarifications!

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Would you like a detailed explanation of this function, or any specific part of it?

Here are five related questions for further exploration:
1. How do you determine the continuity of this piecewise function at \(x = 0\) and \(x = 2\)?
2. What is the derivative of this function in each interval?
3. How do you graph piecewise functions?
4. How can you check for differentiability at \(x = 0\) and \(x = 2\)?
5. What are the real-world applications of piecewise functions?

**Tip:** Always ensure that piecewise functions match up at their boundaries to check for continuity.

Learn how to graph a piecewise function that includes a quadratic, linear, and constant function. This problem involves breaking down the function into three intervals and graphing each segment separately. Suitable for high school students studying algebra and precalculus.

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