Understanding Piecewise Function f(x) with Different Conditions

Math Problem Statement

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:

\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.

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Piecewise Functions
Basic Algebra

f(x) = { x + 1 if x < 0, x - 1 if x > 0 }

Definition of Piecewise Functions

Grades 9-12

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