https://file.aiquickdraw.com/mathbot/file/1729878178211jvdi6wc5.jpg

The function in the image is a piecewise function \( f(x) \) defined as follows:

\[
f(x) =
\begin{cases} 
3 - x & , \ x < 2 \\
3 & , \ x = 2 \\
-x^2 + 4 & , \ x > 2 
\end{cases}
\]

This means:
- For \( x < 2 \), the function is \( f(x) = 3 - x \).
- For \( x = 2 \), the function is a constant, \( f(x) = 3 \).
- For \( x > 2 \), the function is a quadratic, \( f(x) = -x^2 + 4 \).

Would you like more details about analyzing the behavior of this piecewise function, such as continuity or graphing?

Here are five related questions you might explore:
1. Is \( f(x) \) continuous at \( x = 2 \)?
2. What is the domain and range of \( f(x) \)?
3. How would you graph this piecewise function?
4. What are the critical points and local extrema of \( f(x) \)?
5. How does the derivative of \( f(x) \) behave in different intervals?

**Tip:** When working with piecewise functions, always check for continuity and differentiability at the points where the function changes form.

The function in the image is a piecewise function f(x) defined as follows:

f(x) =
{
3 - x , x < 2
3 , x = 2
-x^2 + 4 , x > 2
}

Explore the properties of a piecewise function defined as f(x) = 3 - x for x < 2, f(x) = 3 at x = 2, and f(x) = -x^2 + 4 for x > 2. Understand key concepts like continuity, function behavior, and graphing for grades 9-12.

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