The given function \( f(x) \) is a piecewise function, meaning that it takes different expressions depending on the value of \( x \).

Here’s the breakdown of the function:

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

### Analysis:
- **For \( x < 0 \):** The function is \( f(x) = x + 1 \). This means you add 1 to \( x \).
- **For \( x > 0 \):** The function is \( f(x) = x - 1 \). This means you subtract 1 from \( x \).

Note: There is no explicit definition of \( f(x) \) at \( x = 0 \), so the function is undefined at that point.

Would you like to explore specific values of \( f(x) \), graph the function, or delve into another related topic?

### 5 Related Questions:
1. What happens to the value of \( f(x) \) as \( x \) approaches zero from the left and right?
2. How can we extend \( f(x) \) to include \( x = 0 \)?
3. What is the derivative of \( f(x) \) for \( x > 0 \) and \( x < 0 \)?
4. Can this function be represented as a continuous function by modifying it at \( x = 0 \)?
5. What does the graph of \( f(x) \) look like?

### Tip:
Piecewise functions can often be extended to make them continuous at points where they are undefined.

Given the function f(x) defined as: f(x) = { x + 1 if x < 0, x - 1 if x > 0 }.

Explore the piecewise function f(x) defined by two expressions depending on the value of x. This problem covers key concepts in piecewise functions and basic algebra, providing insights into function behavior for x < 0 and x > 0. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation