Math Problem Statement
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Solution
Here is a piecewise function for you to solve:
3x + 2 & \text{if } x < 0 \\ x^2 - 4 & \text{if } 0 \leq x \leq 2 \\ 2x + 1 & \text{if } x > 2 \end{cases}$$ Let's solve for the following: 1. $$f(-3)$$ 2. $$f(1)$$ 3. $$f(3)$$ ### Solutions: 1. **For $$f(-3)$$:** Since $$-3 < 0$$, we use the first part of the function $$f(x) = 3x + 2$$: $$f(-3) = 3(-3) + 2 = -9 + 2 = -7$$ 2. **For $$f(1)$$:** Since $$0 \leq 1 \leq 2$$, we use the second part of the function $$f(x) = x^2 - 4$$: $$f(1) = 1^2 - 4 = 1 - 4 = -3$$ 3. **For $$f(3)$$:** Since $$3 > 2$$, we use the third part of the function $$f(x) = 2x + 1$$: $$f(3) = 2(3) + 1 = 6 + 1 = 7$$ So the solutions are: 1. $$f(-3) = -7$$ 2. $$f(1) = -3$$ 3. $$f(3) = 7$$ Would you like more details or have any questions? Here are 8 related questions to expand on this information: 1. How do you determine which part of a piecewise function to use for a given value of $$x$$? 2. What is the domain of the given piecewise function? 3. How would you graph the given piecewise function? 4. What is the range of the given piecewise function? 5. How do you find the points of discontinuity in a piecewise function? 6. Can a piecewise function be continuous everywhere? Provide an example. 7. How do you find the derivative of a piecewise function? 8. What are some real-life applications of piecewise functions? **Tip:** When solving piecewise functions, always carefully determine which part of the function applies to the given input value to avoid mistakes.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Domain and Range
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12