Math Problem Statement
For the piecewise function g(x), find the values g(-3), g(3), and g(8) where g(x) = { x + 6 for x ≤ 3; 8 - x for x > 3 }
Solution
Let's break down the piecewise function :
\begin{cases} x + 6 & \text{if } x \leq 3 \\ 8 - x & \text{if } x > 3 \end{cases}$$ We are asked to find $$g(-3)$$, $$g(3)$$, and $$g(8)$$. ### 1. Finding $$g(-3)$$: Since $$-3 \leq 3$$, we use the first part of the piecewise function: $$g(-3) = -3 + 6 = 3$$ ### 2. Finding $$g(3)$$: Since $$3 \leq 3$$, we again use the first part of the piecewise function: $$g(3) = 3 + 6 = 9$$ ### 3. Finding $$g(8)$$: Since $$8 > 3$$, we use the second part of the piecewise function: $$g(8) = 8 - 8 = 0$$ ### Final Answers: $$g(-3) = 3, \quad g(3) = 9, \quad g(8) = 0$$ Would you like further details or have any questions about this? Here are five related questions to expand your understanding: 1. How do you determine which part of a piecewise function to use for a given input? 2. Can a piecewise function be discontinuous? If so, what does that look like? 3. How would you graph the given piecewise function $$g(x)$$? 4. What would $$g(x)$$ equal if $$x = 5$$? 5. How can piecewise functions be applied in real-world scenarios? **Tip**: Always check the condition for each interval of a piecewise function before solving for specific values.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Formulas
For x ≤ 3: g(x) = x + 6
For x > 3: g(x) = 8 - x
Theorems
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Suitable Grade Level
Grades 7-10