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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![### Understanding the Range of a Function and its Transformation
**Problem Statement:**
The range of the function \( R(s) \) is \( 130 \leq R(s) \leq 210 \). What is the range of \( R(s) - 120 \)?
**Task:**
Given the range of the function \( R(s) \), we are to determine the range of the transformed function \( R(s) - 120 \).
#### Solution:
1. **Original Range:**
\[
130 \leq R(s) \leq 210
\]
2. **Transforming the Range:**
To find the range of \( R(s) - 120 \), we subtract 120 from each part of the inequality above:
\[
130 - 120 \leq R(s) - 120 \leq 210 - 120
\]
3. **Simplifying:**
\[
10 \leq R(s) - 120 \leq 90
\]
Therefore, the range of \( R(s) - 120 \) is:
\[
10 \leq R(s) - 120 \leq 90
\]
**Text Explanation:**
- **Input Fields:** Two input boxes are provided for the student to enter the lower and upper bounds of the transformed function range.
#### Additional Resources:
- **eTextbook and Media:** Additional learning materials and resources are available to understand the concept better.
- **Hint:** A hint option is provided to offer assistance if needed.
**Note:** Ensure to save your work for later using the 'Save for Later' button.
**Visual aide:** There are no graphs or diagrams present in this problem.
#### Conclusion:
Understanding how the range of a function is affected by transformations is crucial in mathematics. This exercise demonstrates how to systematically apply transformations to function ranges.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F660a15be-f1ca-4f1d-9222-efc14cd423b5%2F6802f644-fb46-40b2-9596-f5a4af154d3a%2Fl6n8m5v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Range of a Function and its Transformation
**Problem Statement:**
The range of the function \( R(s) \) is \( 130 \leq R(s) \leq 210 \). What is the range of \( R(s) - 120 \)?
**Task:**
Given the range of the function \( R(s) \), we are to determine the range of the transformed function \( R(s) - 120 \).
#### Solution:
1. **Original Range:**
\[
130 \leq R(s) \leq 210
\]
2. **Transforming the Range:**
To find the range of \( R(s) - 120 \), we subtract 120 from each part of the inequality above:
\[
130 - 120 \leq R(s) - 120 \leq 210 - 120
\]
3. **Simplifying:**
\[
10 \leq R(s) - 120 \leq 90
\]
Therefore, the range of \( R(s) - 120 \) is:
\[
10 \leq R(s) - 120 \leq 90
\]
**Text Explanation:**
- **Input Fields:** Two input boxes are provided for the student to enter the lower and upper bounds of the transformed function range.
#### Additional Resources:
- **eTextbook and Media:** Additional learning materials and resources are available to understand the concept better.
- **Hint:** A hint option is provided to offer assistance if needed.
**Note:** Ensure to save your work for later using the 'Save for Later' button.
**Visual aide:** There are no graphs or diagrams present in this problem.
#### Conclusion:
Understanding how the range of a function is affected by transformations is crucial in mathematics. This exercise demonstrates how to systematically apply transformations to function ranges.
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