Given the function k(x) - Calculate the following values: k( – 9) = k(2) = k(4) = k( − 8) = k( − 1) = k(6) = = = - 4x - 7 2x²x9 - 2x + 1 100 x < -1 −1 < x≤ 4 x > 4
Given the function k(x) - Calculate the following values: k( – 9) = k(2) = k(4) = k( − 8) = k( − 1) = k(6) = = = - 4x - 7 2x²x9 - 2x + 1 100 x < -1 −1 < x≤ 4 x > 4
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Piecewise Function and Evaluation
Given the function \( k(x) \):
\[
k(x) = \begin{cases}
-4x - 7 & \text{ if } x \leq -1 \\
2x^2 - x - 9 & \text{ if } -1 < x \leq 4 \\
-2x + 1 & \text{ if } x > 4
\end{cases}
\]
Calculate the following values:
1. \( k(-9) = \) \_\_\_\_\_\_\_\_\_\_
2. \( k(2) = \) \_\_\_\_\_\_\_\_\_\_
3. \( k(4) = \) \_\_\_\_\_\_\_\_\_\_
4. \( k(-8) = \) \_\_\_\_\_\_\_\_\_\_
5. \( k(-1) = \) \_\_\_\_\_\_\_\_\_\_
6. \( k(6) = \) \_\_\_\_\_\_\_\_\_\_
### Explanation
This function, \( k(x) \), is defined in a piecewise manner with different expressions depending on the value of \( x \). Follow the rules below to calculate the function value for a given \( x \):
1. If \( x \) is less than or equal to -1, use the formula: \( -4x - 7 \).
2. If \( x \) is greater than -1 but less than or equal to 4, use the formula: \( 2x^2 - x - 9 \).
3. If \( x \) is greater than 4, use the formula: \( -2x + 1 \).
To find the value of \( k(x) \) for a particular \( x \):
- **For \( k(-9) \)**:
- Since \( -9 \leq -1 \), use \( -4x - 7 \):
\[
k(-9) = -4(-9) - 7 = 36 - 7 = 29
\]
- **For \( k(2) \)**:
- Since \( -1 < 2 \leq 4 \), use \( 2x^2 - x - 9 \):
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc94e4e1c-3d4e-4486-b985-b30353acec86%2F3e4dec36-cd74-4cc5-9988-5a93d489baf0%2F6slafi_processed.png&w=3840&q=75)
Transcribed Image Text:### Piecewise Function and Evaluation
Given the function \( k(x) \):
\[
k(x) = \begin{cases}
-4x - 7 & \text{ if } x \leq -1 \\
2x^2 - x - 9 & \text{ if } -1 < x \leq 4 \\
-2x + 1 & \text{ if } x > 4
\end{cases}
\]
Calculate the following values:
1. \( k(-9) = \) \_\_\_\_\_\_\_\_\_\_
2. \( k(2) = \) \_\_\_\_\_\_\_\_\_\_
3. \( k(4) = \) \_\_\_\_\_\_\_\_\_\_
4. \( k(-8) = \) \_\_\_\_\_\_\_\_\_\_
5. \( k(-1) = \) \_\_\_\_\_\_\_\_\_\_
6. \( k(6) = \) \_\_\_\_\_\_\_\_\_\_
### Explanation
This function, \( k(x) \), is defined in a piecewise manner with different expressions depending on the value of \( x \). Follow the rules below to calculate the function value for a given \( x \):
1. If \( x \) is less than or equal to -1, use the formula: \( -4x - 7 \).
2. If \( x \) is greater than -1 but less than or equal to 4, use the formula: \( 2x^2 - x - 9 \).
3. If \( x \) is greater than 4, use the formula: \( -2x + 1 \).
To find the value of \( k(x) \) for a particular \( x \):
- **For \( k(-9) \)**:
- Since \( -9 \leq -1 \), use \( -4x - 7 \):
\[
k(-9) = -4(-9) - 7 = 36 - 7 = 29
\]
- **For \( k(2) \)**:
- Since \( -1 < 2 \leq 4 \), use \( 2x^2 - x - 9 \):
\
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