https://file.aiquickdraw.com/mathbot/file/1727113814630uq4vitnh.jpg

The image shows a piecewise function \( f(x) \) defined as:

\[
f(x) = \begin{cases}
2x + 1, & \text{if } x < 0 \\
2x + 2, & \text{if } x \geq 0
\end{cases}
\]

This means that the function takes different expressions depending on whether \( x \) is less than 0 or greater than or equal to 0.

- When \( x < 0 \), the function is \( f(x) = 2x + 1 \).
- When \( x \geq 0 \), the function is \( f(x) = 2x + 2 \).

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

Here are 5 related questions you can explore:

1. How do you graph a piecewise function?
2. What are the domain and range of this function?
3. Is this piecewise function continuous? Why or why not?
4. How do you evaluate this function for a specific value of \( x \)?
5. How can we find the derivative of this piecewise function?

**Tip**: When graphing piecewise functions, plot each piece on its respective interval and ensure you indicate whether endpoints are included or excluded using open or closed circles.

The image shows a piecewise function f(x) defined as:

f(x) = { 2x + 1, for x < 0 and 2x + 2, for x ≥ 0 }

Explore the analysis of a piecewise function f(x) defined as 2x + 1 for x < 0 and 2x + 2 for x ≥ 0. Learn about key mathematical concepts such as linear functions, evaluating piecewise functions, and determining continuity. Suitable for high school students in Grades 9-12.

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