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 d from school. A reasonable domain for this function would be 1. positive integers 2. positive real numbers
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 d from school. A reasonable domain for this function would be 1. positive integers 2. positive real numbers
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.1: Concept Of A Function
Problem 99PS
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2015ce15-a78f-4f65-9569-328622639175%2Fcef1790b-0d09-49ae-b544-b7c7cfb80b8f%2F16s33e_processed.jpeg&w=3840&q=75)
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 step
Solved 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.Recommended textbooks for you
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
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