Piecewise Function Definition and Evaluation: f(x) = {x + 1, 3, x

Math Problem Statement

f()={x+1 ifx <0 3 ifx=0 x-2 ifx>0

The function you've provided appears to be a piecewise function. I'll rewrite it with proper formatting:

\begin{cases} x + 1 & \text{if } x < 0 \\ 3 & \text{if } x = 0 \\ x - 2 & \text{if } x > 0 \end{cases}$$ ### Explanation: - **If $$x < 0$$**, the function evaluates as $$f(x) = x + 1$$. - **If $$x = 0$$**, the function evaluates as $$f(x) = 3$$. - **If $$x > 0$$**, the function evaluates as $$f(x) = x - 2$$. Would you like me to evaluate this function at specific points or explain how it behaves over different intervals? Here are 5 related questions to deepen your understanding: 1. What is the value of $$f(-2)$$ using the piecewise function? 2. How does the function behave as $$x \to 0$$ from both the left and the right? 3. What is the graph of this piecewise function like? 4. How would you describe the continuity of $$f(x)$$? 5. How can you modify the function so that it is continuous for all $$x$$? **Tip:** Piecewise functions often change behavior at specific points. Always carefully check which condition applies when calculating values!

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Piecewise Functions
Basic Algebra
Function Evaluation

f(x) = x + 1, for x < 0
f(x) = 3, for x = 0
f(x) = x - 2, for x > 0

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