Math Problem Statement
f(x) is defined as a piecewise function: f(x) = 2x - 1 if x < 1 and f(x) = -x + 3 if x ≥ 1. Find f(-4), f(-2), f(1), and f(4).
Solution
The given function is defined as a piecewise function:
\begin{cases} 2x - 1 & \text{if } x < 1 \\ -x + 3 & \text{if } x \geq 1 \end{cases}$$ We need to evaluate $$f(x)$$ at different values. 1. **$$f(-4)$$**: Since $$-4 < 1$$, we use the first piece of the function, $$f(x) = 2x - 1$$: $$f(-4) = 2(-4) - 1 = -8 - 1 = -9$$ 2. **$$f(-2)$$**: Since $$-2 < 1$$, we use the first piece again: $$f(-2) = 2(-2) - 1 = -4 - 1 = -5$$ 3. **$$f(1)$$**: Since $$1 \geq 1$$, we use the second piece of the function, $$f(x) = -x + 3$$: $$f(1) = -(1) + 3 = -1 + 3 = 2$$ 4. **$$f(4)$$**: Since $$4 \geq 1$$, we use the second piece again: $$f(4) = -(4) + 3 = -4 + 3 = -1$$ The values are: $$f(-4) = -9, \quad f(-2) = -5, \quad f(1) = 2, \quad f(4) = -1$$ Would you like more details or have any questions? Here are some related questions to explore further: 1. How would you graph this piecewise function? 2. What is the domain and range of $$f(x)$$? 3. How does changing the function to $$f(x) = 2x + 1$$ for $$x < 1$$ affect the outputs? 4. Can you find where the function $$f(x)$$ equals zero? 5. What are the properties of piecewise functions that make them useful for modeling real-life situations? **Tip:** When working with piecewise functions, always pay attention to the conditions for each piece to determine which expression to use.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Substitution
Linear Functions
Formulas
f(x) = 2x - 1 if x < 1
f(x) = -x + 3 if x ≥ 1
Theorems
Piecewise Function Evaluation
Suitable Grade Level
Grades 9-10