Math Problem Statement
Given the function f(x) = { 7x - 1 for x < 0; 7x - 2 for x >= 0 }, calculate the following values: f(-1), f(0), f(2).
Solution
The given piecewise function is:
\begin{cases} 7x - 1 & \text{if } x < 0 \\ 7x - 2 & \text{if } x \geq 0 \end{cases}$$ We need to calculate the values of $$f(-1)$$, $$f(0)$$, and $$f(2)$$. 1. **Calculating $$f(-1)$$:** Since $$-1 < 0$$, we use the first part of the function: $$f(-1) = 7(-1) - 1 = -7 - 1 = -8$$ 2. **Calculating $$f(0)$$:** Since $$0 \geq 0$$, we use the second part of the function: $$f(0) = 7(0) - 2 = 0 - 2 = -2$$ 3. **Calculating $$f(2)$$:** Since $$2 \geq 0$$, we use the second part of the function: $$f(2) = 7(2) - 2 = 14 - 2 = 12$$ ### Final Answers: - $$f(-1) = -8$$ - $$f(0) = -2$$ - $$f(2) = 12$$ Would you like further explanations on these calculations, or do you have any other questions? ### Related Questions: 1. How do you determine which part of a piecewise function to use? 2. What happens if you input a value exactly at the boundary of a piecewise function? 3. How can you graph a piecewise function? 4. How do piecewise functions apply in real-world scenarios? 5. What are the common mistakes when evaluating piecewise functions? ### Tip: Always double-check the conditions of a piecewise function to ensure you are using the correct formula for the given input value.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Formulas
f(x) = { 7x - 1 if x < 0; 7x - 2 if x >= 0 }
Theorems
-
Suitable Grade Level
Grades 7-10