The function \( f(x) = x + 1 \) with the condition \( x < 1 \) defines a piecewise function. However, you've only provided the rule for \( x < 1 \). Usually, in piecewise functions, other rules define the behavior of \( f(x) \) when \( x \geq 1 \).

For example, the complete function could look like:

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

Could you clarify or provide more information about \( f(x) \) for \( x \geq 1 \)?

If you want to ask any specific questions about this function or piecewise functions, feel free!

Here are 5 relative questions to expand on this:

1. What happens to the function when \( x \geq 1 \)?
2. How would you graph the function \( f(x) = x + 1 \) for \( x < 1 \)?
3. Can you provide an example of a complete piecewise function that includes a rule for \( x \geq 1 \)?
4. What is the importance of defining conditions for different ranges of \( x \) in piecewise functions?
5. How do you evaluate the continuity of a piecewise function at a specific point?

**Tip:** In piecewise functions, always check for continuity or any possible jumps at the boundaries where the function definition changes (e.g., \( x = 1 \) in your case).

Explore the piecewise function f(x) = x + 1 for x < 1. This problem focuses on key concepts such as piecewise function definition, inequalities, and continuity at boundary points. Suitable for high school students in Grades 9-12.

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