Graphing Piecewise Function with Quadratic, Linear, and Constant Segments

Math Problem Statement

draw this Piecewise function

Draw this piecewise function.

The piecewise function you've provided can be described as:

\begin{cases} x^2 - 1 & \text{for } x < 0 \\ -x + 2 & \text{for } 0 \leq x < 2 \\ 2 & \text{for } x \geq 2 \end{cases}$$ Let me know if you'd like to graph this function or have any further clarifications! --- Would you like a detailed explanation of this function, or any specific part of it? Here are five related questions for further exploration: 1. How do you determine the continuity of this piecewise function at $$x = 0$$ and $$x = 2$$? 2. What is the derivative of this function in each interval? 3. How do you graph piecewise functions? 4. How can you check for differentiability at $$x = 0$$ and $$x = 2$$? 5. What are the real-world applications of piecewise functions? **Tip:** Always ensure that piecewise functions match up at their boundaries to check for continuity.

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Piecewise Functions
Quadratic Functions
Linear Functions
Constant Functions

f(x) = x^2 - 1 for x < 0
f(x) = -x + 2 for 0 ≤ x < 2
f(x) = 2 for x ≥ 2

Continuity of functions
Differentiability of piecewise functions

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