Piecewise Function Analysis: -2, -2x-1, and 0

Math Problem Statement

and 3 if <-2 -2x-1 if 2<x<1 0 if x>1

It looks like you've defined a piecewise function. Let me clarify it and express it properly:

\begin{cases} -2 & \text{if } x \leq -2 \\ -2x - 1 & \text{if } -2 < x \leq 1 \\ 0 & \text{if } x > 1 \end{cases}$$ To break it down: 1. **For $$x \leq -2$$:** $$f(x) = -2$$ 2. **For $$-2 < x \leq 1$$:** $$f(x) = -2x - 1$$ 3. **For $$x > 1$$:** $$f(x) = 0$$ If this is correct, let me know how you'd like to proceed! I can help you analyze this function further or perform operations like evaluating it at specific points, finding limits, or graphing it. Would you like more details or clarifications? Here are 5 possible related questions to explore: 1. How do you graph a piecewise function? 2. How do you find the domain and range of a piecewise function? 3. How would you compute the limit of this function as $$x$$ approaches certain points (e.g., $$x = 1$$)? 4. How can we determine whether this function is continuous at $$x = -2$$ and $$x = 1$$? 5. What does the derivative of this piecewise function look like? **Tip:** For any piecewise function, it's important to check for continuity at the transition points where the pieces meet!

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Piecewise Functions
Linear Functions
Inequalities

f(x) = -2 if x <= -2
f(x) = -2x - 1 if -2 < x <= 1
f(x) = 0 if x > 1

Continuity Theorem for Piecewise Functions
Limit Theorems

Grades 9-12

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