Math Problem Statement
Find f(3) for this piecewise-defined function.
Solution
The given piecewise-defined function is:
\begin{cases} -\frac{2}{7}x + 4 & \text{if } x < 3 \\ 8x - 9 & \text{if } x \geq 3 \end{cases}$$ We are asked to find $$f(3)$$. Since $$x = 3$$, we will use the second part of the piecewise function because it applies to $$x \geq 3$$: $$f(x) = 8x - 9$$ Substitute $$x = 3$$: $$f(3) = 8(3) - 9 = 24 - 9 = 15$$ Thus, $$f(3) = 15$$. Would you like further clarification on this? Here are five related questions for further practice: 1. What is $$f(2)$$ for the same function? 2. How would the function change if the condition were $$x \leq 3$$ instead of $$x \geq 3$$? 3. What is the slope of the function $$f(x) = -\frac{2}{7}x + 4$$? 4. If the piecewise function changed to $$f(x) = 8x - 12$$ for $$x \geq 3$$, what would $$f(3)$$ be? 5. What is the domain of the piecewise function? **Tip**: Always check the condition associated with the piecewise function to ensure you're using the correct part of the function for the given input.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Substitution
Formulas
f(x) = -2/7 * x + 4 for x < 3
f(x) = 8x - 9 for x >= 3
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 9-10