https://file.aiquickdraw.com/mathbot/file/1726786944432faw2p2ml.jpg

The image shows a piecewise function defined as:

\[
f(x) =
\begin{cases} 
b - 2x & \text{if } x < 2 \\
\frac{24}{x - b} & \text{if } x \geq 2 
\end{cases}
\]

If you have any specific questions about this function, such as finding limits, continuity, or other properties, feel free to ask!

Would you like more details on how to analyze this function?

Here are five follow-up questions you might consider:
1. What is the value of \( b \) if \( f(x) \) needs to be continuous at \( x = 2 \)?
2. How can we calculate the derivative of \( f(x) \) in both cases?
3. Can we find the limit of \( f(x) \) as \( x \) approaches 2 from both sides?
4. What is the domain of this function?
5. What happens to \( f(x) \) as \( x \) approaches infinity?

**Tip**: When working with piecewise functions, it's often helpful to check for continuity and differentiability at the boundary point (in this case, \( x = 2 \)).

Let f(x) = { b - 2x if x < 2; 24 / (x - b) if x ≥ 2.}

Explore the properties of a piecewise function defined as f(x) = { b - 2x if x < 2; 24 / (x - b) if x ≥ 2}. This function involves key concepts such as limits, continuity at x = 2, and piecewise behavior. Learn how to analyze its behavior and solve for continuity and limits.

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