Math Problem Statement
What is the piecewise function f(x) defined in the image, and how is it evaluated for different values of x?
Solution
The image shows a piecewise function defined as follows:
\begin{cases} 2, & \text{for } x \leq 1 \\ -2x, & \text{for } x \geq -1 \end{cases}$$ ### Explanation: 1. For $$x \leq 1$$, the function $$f(x)$$ is constant with $$f(x) = 2$$. 2. For $$x \geq -1$$, the function $$f(x) = -2x$$, which is a linear function with a slope of $$-2$$. Would you like further details on analyzing the behavior of this piecewise function, such as sketching it or finding specific values? --- Here are five related questions for further exploration: 1. What is the value of $$f(x)$$ at the boundary points, such as $$x = 1$$ and $$x = -1$$? 2. How does the function behave as $$x \to \infty$$ and $$x \to -\infty$$ for each piece? 3. What would the graph of this piecewise function look like, and how would it change at the boundaries? 4. Is $$f(x)$$ continuous at $$x = 1$$ and $$x = -1$$? 5. How does the slope of the line in the second part affect the shape of the graph? **Tip:** When dealing with piecewise functions, always pay close attention to the conditions for each piece to understand how the function behaves at different intervals.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Linear Functions
Formulas
f(x) = { 2 for x <= 1; -2x for x >= -1 }
Theorems
Properties of Piecewise Functions
Suitable Grade Level
Grades 10-12