Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Understanding Piecewise Functions**
In this exercise, you will use a piecewise-defined function to find specific values for \( f(x) \).
### Problem Statement
You are given a piecewise function defined as follows:
- \( f(x) = 2 - 4x \) if \( x \leq 2 \)
- \( f(x) = 2x \) if \( 2 < x < 6 \)
- \( f(x) = 4x + 5 \) if \( x \geq 6 \)
Calculate the value of \( f(0) \).
### Instructions
1. **Identify the appropriate piece.** For \( x = 0 \), determine which piece of the function applies by checking the conditions:
- Since \( 0 \leq 2 \), use \( f(x) = 2 - 4x \).
2. **Calculate \( f(0) \).**
- Substitute \( x = 0 \) into the equation:
\[ f(0) = 2 - 4(0) = 2. \]
Therefore, the value of \( f(0) \) is 2.
### Additional Help
For further assistance, refer to similar examples or ask for guidance to better understand how to work with piecewise functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84f905e7-8d15-44f1-8ba1-68b7e3fd4c33%2Fb8fa4456-3967-46e4-84ba-22e67312b6e1%2F6hhyj77_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Piecewise Functions**
In this exercise, you will use a piecewise-defined function to find specific values for \( f(x) \).
### Problem Statement
You are given a piecewise function defined as follows:
- \( f(x) = 2 - 4x \) if \( x \leq 2 \)
- \( f(x) = 2x \) if \( 2 < x < 6 \)
- \( f(x) = 4x + 5 \) if \( x \geq 6 \)
Calculate the value of \( f(0) \).
### Instructions
1. **Identify the appropriate piece.** For \( x = 0 \), determine which piece of the function applies by checking the conditions:
- Since \( 0 \leq 2 \), use \( f(x) = 2 - 4x \).
2. **Calculate \( f(0) \).**
- Substitute \( x = 0 \) into the equation:
\[ f(0) = 2 - 4(0) = 2. \]
Therefore, the value of \( f(0) \) is 2.
### Additional Help
For further assistance, refer to similar examples or ask for guidance to better understand how to work with piecewise functions.
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