Jonathan makes a weekly allowance of $25. He also makes $9.50 an hours at his job. Because of his age, Jonathan can work no more than 20 hours per week Type here a) Write a function for the amount of money he makes cach week based on the amount of hours, A, he works. Type here What is the demain of the function for this situation? Type here c) Sketch the graph of the function over the domain you chose.

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Title: Calculating Weekly Earnings Based on Hours Worked**

**Description:**
Jonathan makes a weekly allowance of $25. He also makes $9.50 an hour at his job. Because of his age, Jonathan can work no more than 20 hours per week.

**Instructions:**

1. **Write a function for the amount of money he makes each week based on the amount of hours, \( h \), he works.**
   
   **Answer:**
   \( M(h) = 25 + 9.5h \)

2. **What is the domain of the function for this situation?**
   
   **Answer:**
   The domain of the function is \( 0 \le h \le 20 \), because Jonathan can work anywhere from 0 to 20 hours per week.

3. **Sketch the graph of the function over the domain you chose.**

**Graph Explanation:**
The x-axis represents the number of hours \( h \) worked per week, ranging from 0 to 20. The y-axis represents the total weekly earnings \( M(h) \). The graph is a straight line starting at the point (0, 25) and ending at (20, 215). This linear graph indicates that each additional hour worked increases the total earnings by $9.50 following the equation \( M(h) = 25 + 9.5h \). The line should be drawn solidly between these points as Jonathan can work any number of hours from 0 to 20.

**Image:**
The document contains a grid with an x and y axis ready to plot the graph. The starting point is at (0, 25) and continues to increase linearly until the endpoint at (20, 215).

**Educational Note:**
This exercise helps understand how linear functions are applied in real-life scenarios such as calculating earnings and understanding domains within practical limits.
Transcribed Image Text:**Title: Calculating Weekly Earnings Based on Hours Worked** **Description:** Jonathan makes a weekly allowance of $25. He also makes $9.50 an hour at his job. Because of his age, Jonathan can work no more than 20 hours per week. **Instructions:** 1. **Write a function for the amount of money he makes each week based on the amount of hours, \( h \), he works.** **Answer:** \( M(h) = 25 + 9.5h \) 2. **What is the domain of the function for this situation?** **Answer:** The domain of the function is \( 0 \le h \le 20 \), because Jonathan can work anywhere from 0 to 20 hours per week. 3. **Sketch the graph of the function over the domain you chose.** **Graph Explanation:** The x-axis represents the number of hours \( h \) worked per week, ranging from 0 to 20. The y-axis represents the total weekly earnings \( M(h) \). The graph is a straight line starting at the point (0, 25) and ending at (20, 215). This linear graph indicates that each additional hour worked increases the total earnings by $9.50 following the equation \( M(h) = 25 + 9.5h \). The line should be drawn solidly between these points as Jonathan can work any number of hours from 0 to 20. **Image:** The document contains a grid with an x and y axis ready to plot the graph. The starting point is at (0, 25) and continues to increase linearly until the endpoint at (20, 215). **Educational Note:** This exercise helps understand how linear functions are applied in real-life scenarios such as calculating earnings and understanding domains within practical limits.
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