Math Problem Statement
Find the values of f(-4), f(3), and f(8) for the piecewise function f(x) = {x - 7 if x ≤ 3, 3 - x if x > 3}.
Solution
Let's analyze the given piecewise function and calculate the required values.
The function is defined as:
x - 7 & \text{if } x \leq 3 \\ 3 - x & \text{if } x > 3 \end{cases}$$ We need to calculate: 1. $$f(-4)$$ 2. $$f(3)$$ 3. $$f(8)$$ ### 1. $$f(-4)$$ Since $$-4 \leq 3$$, we use the first part of the piecewise function: $$f(-4) = -4 - 7 = -11$$ ### 2. $$f(3)$$ Since $$3 \leq 3$$, we use the first part of the piecewise function again: $$f(3) = 3 - 7 = -4$$ ### 3. $$f(8)$$ Since $$8 > 3$$, we use the second part of the piecewise function: $$f(8) = 3 - 8 = -5$$ ### Final Answers: $$f(-4) = -11, \quad f(3) = -4, \quad f(8) = -5$$ Would you like more details on this? Here are 5 related questions that might help expand your understanding: 1. How do we determine which part of the piecewise function to use? 2. What is a piecewise function, and why is it useful? 3. What happens when $$f(x)$$ has more than two pieces? 4. Can you plot a graph of this piecewise function to visualize it? 5. How would the function change if we modified the conditions (e.g., changing $$x \leq 3$$ to $$x < 3$$)? **Tip:** When working with piecewise functions, always pay close attention to the boundary values of each condition to choose the correct formula!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Formulas
f(x) = x - 7 if x ≤ 3
f(x) = 3 - x if x > 3
Theorems
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Suitable Grade Level
Grades 8-10