Algebra for College Students
10th Edition
ISBN: 9781285195780
Author: Jerome E. Kaufmann, Karen L. Schwitters
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Question
![***Educational Content on Reasonable Domains for Functions***
**Problem Statement:**
\[ \text{[School Name]} \]Senior High School uses the function \(f(s)\), where \(s\) is the number of students, to model how many students have late arrival or early dismissal from school. A reasonable domain for this function would be:
1. positive integers
2. positive real numbers
3. negative real numbers
4. both positive and negative real numbers.
**Explanation:**
In this scenario, the function \(f(s)\) maps the number of students \(s\) to the count of students who arrive late or leave early. Let's analyze each option for the domain:
1. **Positive Integers:**
Positive integers are suitable for modeling the number of students because you cannot have a fraction or decimal of a student. The count starts from 1 and goes upwards (1, 2, 3, ...).
2. **Positive Real Numbers:**
Positive real numbers include all positive fractions and decimals, which are not practical in this context since the number of students is always a whole number.
3. **Negative Real Numbers:**
Negative numbers do not make sense in this context because you cannot have a negative count of students.
4. **Both Positive and Negative Real Numbers:**
Including both positive and negative real numbers is not practical here because while positive numbers represent a realistic count of students, negative numbers do not have any meaningful interpretation within this context.
Hence, the most appropriate domain for the function \(f(s)\) is **positive integers** (Option 1).
---
Note: The text has been adapted to ensure relevance and clarity for educational purposes, focusing on understanding the practical application of domains in mathematical modeling.](https://content.bartleby.com/qna-images/question/2015ce15-a78f-4f65-9569-328622639175/cef1790b-0d09-49ae-b544-b7c7cfb80b8f/16s33e_processed.jpeg)
Transcribed Image Text:***Educational Content on Reasonable Domains for Functions***
**Problem Statement:**
\[ \text{[School Name]} \]Senior High School uses the function \(f(s)\), where \(s\) is the number of students, to model how many students have late arrival or early dismissal from school. A reasonable domain for this function would be:
1. positive integers
2. positive real numbers
3. negative real numbers
4. both positive and negative real numbers.
**Explanation:**
In this scenario, the function \(f(s)\) maps the number of students \(s\) to the count of students who arrive late or leave early. Let's analyze each option for the domain:
1. **Positive Integers:**
Positive integers are suitable for modeling the number of students because you cannot have a fraction or decimal of a student. The count starts from 1 and goes upwards (1, 2, 3, ...).
2. **Positive Real Numbers:**
Positive real numbers include all positive fractions and decimals, which are not practical in this context since the number of students is always a whole number.
3. **Negative Real Numbers:**
Negative numbers do not make sense in this context because you cannot have a negative count of students.
4. **Both Positive and Negative Real Numbers:**
Including both positive and negative real numbers is not practical here because while positive numbers represent a realistic count of students, negative numbers do not have any meaningful interpretation within this context.
Hence, the most appropriate domain for the function \(f(s)\) is **positive integers** (Option 1).
---
Note: The text has been adapted to ensure relevance and clarity for educational purposes, focusing on understanding the practical application of domains in mathematical modeling.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- How do you find the value of a function?arrow_forwardHow do you find the domain for the composition of two functions, fg ?arrow_forwardHow do the graphs of the functions f(x)=x2 and f(x)=x21 differ? We graphed them at the start of this section. What is the difference between their graphs? How are their graphs the same?arrow_forward
- During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?arrow_forwardIn your own words, explain the difference betweena relation and a function.arrow_forwardSuppose the range of a function fis [5,8] . What is the range of |f(x)| ?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Intermediate Algebra
Algebra
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage