***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 integers2. positive real numbers3. negative real numbers4. 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.

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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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section9.9: Combining Functions

Problem 11CYU

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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.

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