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The cost of holding a children's birthday party at a rollerskating rink is a function of n, the number of people in the party. The cost function, C, can be represented with this set of rules 150, 0

The cost of holding a children's birthday party at a rollerskating rink is a function of n, the number of people in the party. The cost function, C, can be represented with this set of rules 150, 0

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
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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The graph on the coordinate plane displays the relationship between the "number of people in the party" on the x-axis and the "cost in dollars" on the y-axis. There are three horizontal lines, each representing a different cost associated with varying numbers of people. 1. **Red Line**: This line is horizontal at $150, indicating that the cost remains constant at $150 regardless of the number of people, within a specific range. 2. **Yellow Line**: This line is horizontal at $250, showing a constant cost of $250 for a different range of people. 3. **Blue Line**: This line is horizontal at $400, representing a constant cost of $400 for the party size in its respective range. The lines suggest a tiered pricing structure where the cost increases in steps as the number of people in the party exceeds certain thresholds. The graph provides an easy way to understand the fixed costs associated with different party sizes.
Transcribed Image Text:The graph on the coordinate plane displays the relationship between the "number of people in the party" on the x-axis and the "cost in dollars" on the y-axis. There are three horizontal lines, each representing a different cost associated with varying numbers of people. 1. **Red Line**: This line is horizontal at $150, indicating that the cost remains constant at $150 regardless of the number of people, within a specific range. 2. **Yellow Line**: This line is horizontal at $250, showing a constant cost of $250 for a different range of people. 3. **Blue Line**: This line is horizontal at $400, representing a constant cost of $400 for the party size in its respective range. The lines suggest a tiered pricing structure where the cost increases in steps as the number of people in the party exceeds certain thresholds. The graph provides an easy way to understand the fixed costs associated with different party sizes.
**Question #5:** The cost of holding a children's birthday party at a rollerskating rink is a function of \( n \), the number of people in the party. The cost function, \( C \), can be represented with this set of rules: \[ C(n) = \begin{cases} 150, & 0 < n \leq 12 \\ 260, & 12 < n \leq 20 \\ 400, & 20 < n \leq 30 \end{cases} \] **Part A**: How much does it cost to have a party with 9 people? What about 20 people? It costs \$150 to have a party with 9 people and it costs \$400 to have a party with 20 people. **Question #5:** **Part B**: Graph the function on the coordinate plane. --- Explanation for an Educational Website: This section describes the cost structure for hosting a children's party at a rollerskating rink, which depends on the number of attendees: 1. **Cost Function Explanation**: - For parties with 1 to 12 people, the cost is \$150. - For parties with 13 to 20 people, the cost is \$260. - For parties with 21 to 30 people, the cost is \$400. 2. **Cost Calculation Examples**: - A party with 9 people falls in the first category, costing \$150. - A party with 20 people falls into the second category, costing \$400. 3. **Graphing Part B**: - The function should be plotted on a graph with the number of people on the x-axis and the cost on the y-axis. You would plot the constant costs across their respective intervals, creating a step function appearance. This representation helps in understanding how the cost scales with the number of attendees, visually reinforcing the concept of piecewise functions.
Transcribed Image Text:**Question #5:** The cost of holding a children's birthday party at a rollerskating rink is a function of \( n \), the number of people in the party. The cost function, \( C \), can be represented with this set of rules: \[ C(n) = \begin{cases} 150, & 0 < n \leq 12 \\ 260, & 12 < n \leq 20 \\ 400, & 20 < n \leq 30 \end{cases} \] **Part A**: How much does it cost to have a party with 9 people? What about 20 people? It costs \$150 to have a party with 9 people and it costs \$400 to have a party with 20 people. **Question #5:** **Part B**: Graph the function on the coordinate plane. --- Explanation for an Educational Website: This section describes the cost structure for hosting a children's party at a rollerskating rink, which depends on the number of attendees: 1. **Cost Function Explanation**: - For parties with 1 to 12 people, the cost is \$150. - For parties with 13 to 20 people, the cost is \$260. - For parties with 21 to 30 people, the cost is \$400. 2. **Cost Calculation Examples**: - A party with 9 people falls in the first category, costing \$150. - A party with 20 people falls into the second category, costing \$400. 3. **Graphing Part B**: - The function should be plotted on a graph with the number of people on the x-axis and the cost on the y-axis. You would plot the constant costs across their respective intervals, creating a step function appearance. This representation helps in understanding how the cost scales with the number of attendees, visually reinforcing the concept of piecewise functions.
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