https://file.aiquickdraw.com/mathbot/file/1725901642899dsw5dbek.jpg

The image shows a piecewise function \( f(x) \) with two cases:

\[
f(x) = 
\begin{cases} 
x - 3 & \text{if } x \leq 2 \\
x^2 - 2x & \text{if } x > 2
\end{cases}
\]

Would you like a detailed explanation of how this function behaves, or is there a specific problem you'd like to address related to it?

Here are some related questions you could explore:
1. What is the domain and range of this piecewise function?
2. How do you evaluate \( f(x) \) for a given \( x \)?
3. Can you graph this piecewise function and analyze its continuity at \( x = 2 \)?
4. How do you find the derivative of the piecewise function?
5. How does the function behave as \( x \) approaches 2 from both sides?

**Tip:** Always check for continuity and differentiability at the points where the definition of a piecewise function changes.

What is the piecewise function defined as shown in the image, and how can we analyze its behavior?

This problem involves analyzing a piecewise function where one segment is linear (x - 3) for x ≤ 2, and the other is quadratic (x^2 - 2x) for x > 2. Explore the function's domain, range, and continuity, and learn how to evaluate and graph the function.

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