Math Problem Statement
For the piecewise function, find the values g(-4), g(2), and g(9). The function is given by: g(x) = { x + 9, for x ≤ 2; 6 - x, for x > 2 }
Solution
The problem asks to find the values of the piecewise function at specific points. The function is given as:
\begin{cases} x + 9, & \text{for } x \leq 2 \\ 6 - x, & \text{for } x > 2 \end{cases}$$ You need to calculate $$g(-4)$$, $$g(2)$$, and $$g(9)$$. ### 1. $$g(-4)$$: Since $$-4 \leq 2$$, use the first part of the piecewise function $$g(x) = x + 9$$: $$g(-4) = -4 + 9 = 5$$ ### 2. $$g(2)$$: Since $$2 \leq 2$$, use the first part of the piecewise function $$g(x) = x + 9$$: $$g(2) = 2 + 9 = 11$$ ### 3. $$g(9)$$: Since $$9 > 2$$, use the second part of the piecewise function $$g(x) = 6 - x$$: $$g(9) = 6 - 9 = -3$$ ### Final Answers: - $$g(-4) = 5$$ - $$g(2) = 11$$ - $$g(9) = -3$$ Would you like further clarification on any part of the solution? Here are five related questions to practice: 1. What is the value of $$g(0)$$ for the same piecewise function? 2. How would you find $$g(3)$$? 3. Can you graph the piecewise function $$g(x)$$? 4. What happens to $$g(x)$$ as $$x$$ approaches infinity? 5. How would you modify the function if the condition for the second part was $$x \geq 3$$ instead of $$x > 2$$? **Tip:** Always check which condition of the piecewise function applies before evaluating it at a specific value of $$x$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Formulas
g(x) = x + 9 for x ≤ 2
g(x) = 6 - x for x > 2
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 7-9