Math Problem Statement
For the piecewise function, find the values g(-6), g(4), and g(8). g(x) = {x + 6 for x ≤ 4, 8 - x for x > 4}
Solution
We are given the piecewise function:
\begin{cases} x + 6 & \text{for } x \leq 4 \\ 8 - x & \text{for } x > 4 \end{cases}$$ We need to evaluate $$g(-6)$$, $$g(4)$$, and $$g(8)$$. ### Step-by-Step Calculations: 1. **For $$g(-6)$$**: Since $$-6 \leq 4$$, we use the first part of the piecewise function: $$g(-6) = -6 + 6 = 0$$ 2. **For $$g(4)$$**: Since $$4 \leq 4$$, we also use the first part of the function: $$g(4) = 4 + 6 = 10$$ 3. **For $$g(8)$$**: Since $$8 > 4$$, we use the second part of the function: $$g(8) = 8 - 8 = 0$$ ### Final Values: $$g(-6) = 0, \quad g(4) = 10, \quad g(8) = 0$$ Let me know if you'd like further details, and here are some related questions to explore: 1. What is $$g(0)$$? 2. What is the domain of the function $$g(x)$$? 3. How does the function behave at the boundary $$x = 4$$? 4. What is the range of $$g(x)$$? 5. How would the function change if the condition for $$x > 4$$ was modified? **Tip**: Always check the condition of a piecewise function to determine which part of the function to use for evaluation.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
g(x) = x + 6 (for x ≤ 4)
g(x) = 8 - x (for x > 4)
Theorems
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Suitable Grade Level
Grades 9-12