https://file.aiquickdraw.com/mathbot/file/172736569720105avtyoo.jpg

The given piecewise function in the image is:

\[
f(x) = \begin{cases} 
x^2, & \text{for } x \leq 2, \\
8 - 2x, & \text{for } 2 < x < 4, \\
4, & \text{for } x \geq 4.
\end{cases}
\]

Would you like help with solving a particular problem related to this function, such as finding its domain, evaluating specific values, or analyzing its continuity?

Here are five related questions:
1. What is the domain and range of the given piecewise function \(f(x)\)?
2. Is \(f(x)\) continuous at \(x = 2\) and \(x = 4\)?
3. How do you find the limit of \(f(x)\) as \(x\) approaches 2 from the left and right?
4. How do you graph this piecewise function?
5. What are the values of \(f(x)\) at \(x = 1, 3, 5\)?

**Tip:** When analyzing a piecewise function, always check the function's behavior at the boundary points where the pieces change.

The given piecewise function is defined as follows: 
1. f(x) = x^2 for x ≤ 2
2. f(x) = 8 - 2x for 2 < x < 4
3. f(x) = 4 for x ≥ 4.

Explore the piecewise function defined as f(x) = x^2 for x ≤ 2, f(x) = 8 - 2x for 2 < x < 4, and f(x) = 4 for x ≥ 4. Learn how to analyze its continuity and limits at the points x = 2 and x = 4. Suitable for high school students in Grades 10-12.

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