Piecewise Function f(x) = 1/2x + 2 and f(x) = -x

Math Problem Statement

f(x) {1/2x+2 uf x > or = -2}and {-x-3 if x<-2}

It seems like you are describing a piecewise function, but there may be a slight formatting issue. Here's how I interpret your function:

\begin{cases} \frac{1}{2}x + 2 & \text{if } x \geq -2 \\ -x - 3 & \text{if } x < -2 \end{cases}$$ This function is defined by two different expressions, depending on the value of $$x$$: 1. If $$x \geq -2$$, the function is $$f(x) = \frac{1}{2}x + 2$$. 2. If $$x < -2$$, the function is $$f(x) = -x - 3$$. ### Would you like to: - Find the value of $$f(x)$$ at a specific point? - Analyze the continuity of this function? - Graph the function? - Investigate the behavior as $$x$$ approaches certain values? Let me know what you'd like to explore! ### Related questions: 1. How do you determine if a piecewise function is continuous? 2. How do you graph a piecewise function step by step? 3. How do you evaluate a piecewise function at a given point? 4. What happens to the value of $$f(x)$$ as $$x$$ approaches -2 from the left and right? 5. How do you compute the derivative of a piecewise function? ### Tip: When dealing with piecewise functions, it's helpful to identify the boundary points (like $$x = -2$$ in this case) and check whether the function is continuous at those points by comparing the left-hand and right-hand limits.

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Piecewise Functions
Algebra

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

Piecewise function definition
Continuity of functions

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