Math Problem Statement

What is m(-3) if the piecewise function is given by: m(x) = { -x if x < -1, 0.5x - 2 if -1 <= x <= 4, x if x > 4 }?

Solution

Let's analyze the piecewise function m(x)m(x) from the image:

\begin{cases} -x & \text{if } x < -1 \\ 0.5x - 2 & \text{if } -1 \leq x \leq 4 \\ x & \text{if } x > 4 \end{cases}$$ We are asked to find $$m(-3)$$. Since $$-3 < -1$$, we use the first case of the function: $$m(x) = -x \quad \text{for} \quad x < -1$$ Substituting $$x = -3$$: $$m(-3) = -(-3) = 3$$ Therefore, $$m(-3) = 3$$. Would you like any additional details on this solution? Here are five related questions: 1. How would the function behave for $$m(2)$$? 2. What is $$m(5)$$ based on the given function? 3. For which $$x$$ does the function equal zero? 4. What is the range of the function over $$-3 \leq x \leq 4$$? 5. How would the graph of this piecewise function look? **Tip**: When working with piecewise functions, always carefully check the domain each piece applies to before selecting which expression to use.

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Math Problem Analysis

Mathematical Concepts

Piecewise functions
Function evaluation

Formulas

m(x) = { -x if x < -1, 0.5x - 2 if -1 <= x <= 4, x if x > 4 }

Theorems

Piecewise function evaluation

Suitable Grade Level

Grades 9-11