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,...
Related questions
Question
![### Piecewise Function Problem
#### Given:
The function \( f(x) \) is defined as:
\[
f(x) =
\begin{cases}
2x - 1 & \text{if } -2 \leq x \leq 5 \\
x^3 - 5 & \text{if } 5 < x \leq 6
\end{cases}
\]
#### Task:
Find the following values:
- (a) \( f(0) \)
- (b) \( f(1) \)
- (c) \( f(5) \)
- (d) \( f(6) \)
#### Explanation:
The function \( f(x) \) is divided into two parts based on the value of \( x \). The first equation, \( 2x - 1 \), applies when \( x \) is between \(-2\) and \(5\), inclusive. The second equation, \( x^3 - 5 \), applies when \( x \) is greater than \(5\) but less than or equal to \(6\).
To solve this, substitute the given \( x \)-values into the appropriate piece of the function based on its definition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F264fb623-143f-42db-a0bb-6b5d4882a9cc%2F83b48616-c1fb-43cf-a8b4-580109b70930%2Fwnt7ozc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Piecewise Function Problem
#### Given:
The function \( f(x) \) is defined as:
\[
f(x) =
\begin{cases}
2x - 1 & \text{if } -2 \leq x \leq 5 \\
x^3 - 5 & \text{if } 5 < x \leq 6
\end{cases}
\]
#### Task:
Find the following values:
- (a) \( f(0) \)
- (b) \( f(1) \)
- (c) \( f(5) \)
- (d) \( f(6) \)
#### Explanation:
The function \( f(x) \) is divided into two parts based on the value of \( x \). The first equation, \( 2x - 1 \), applies when \( x \) is between \(-2\) and \(5\), inclusive. The second equation, \( x^3 - 5 \), applies when \( x \) is greater than \(5\) but less than or equal to \(6\).
To solve this, substitute the given \( x \)-values into the appropriate piece of the function based on its definition.
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