Solve Piecewise Function Problems with Detailed Examples

Math Problem Statement

create me a piecewise function so I can solve it

Sure, here's a piecewise function for you to solve:

x^2 + 2x + 1 & \text{if } x < 0 \\ 3x + 4 & \text{if } 0 \leq x < 5 \\ 2x - 1 & \text{if } x \geq 5 \end{cases}$$ Let's solve for $$f(x)$$ at specific values: 1. $$f(-2)$$ 2. $$f(0)$$ 3. $$f(3)$$ 4. $$f(5)$$ 5. $$f(7)$$ ### Solutions: 1. **$$f(-2)$$**: Since $$-2 < 0$$, $$f(-2) = (-2)^2 + 2(-2) + 1 = 4 - 4 + 1 = 1$$ 2. **$$f(0)$$**: Since $$0 \leq x < 5$$, $$f(0) = 3(0) + 4 = 0 + 4 = 4$$ 3. **$$f(3)$$**: Since $$0 \leq x < 5$$, $$f(3) = 3(3) + 4 = 9 + 4 = 13$$ 4. **$$f(5)$$**: Since $$x \geq 5$$, $$f(5) = 2(5) - 1 = 10 - 1 = 9$$ 5. **$$f(7)$$**: Since $$x \geq 5$$, $$f(7) = 2(7) - 1 = 14 - 1 = 13$$ Do you want details on any of these calculations, or do you have any questions? ### Related Questions: 1. How do you define a piecewise function? 2. What is the domain of a piecewise function? 3. How do you find the range of a piecewise function? 4. How do you graph a piecewise function? 5. How do you solve for the derivative of a piecewise function? 6. How do you solve for the integral of a piecewise function? 7. How do you determine if a piecewise function is continuous? 8. What are the applications of piecewise functions in real life? ### Tip: When dealing with piecewise functions, always pay attention to the defined intervals to ensure you're using the correct expression for each segment of the function.

Drop file here or Click Here to upload

Piecewise Functions
Function Evaluation

Grades 10-12

Solve Piecewise Function Problems: Detailed Step-by-Step Solutions

Analyzing Piecewise Functions: Problems and Solutions

Understanding Piecewise Functions and Their Application

Solving and Graphing a Piecewise Function: Domain, Range, and Function Values

Understanding Piecewise Functions: Key Points and Examples